INVERSE MATERIALS PROPERTIES PREDICTION BASE ON THE VICKERS AND SPHERICAL INDENTATIONS.

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INVERSE MATE

PREDICTION BA

SPHERICAL IND

Ir. I Nyoman Bud

ERIALS PROPERTIES

BASE ON THE VICKER

DENTATIONS

udiarsa, MT, Ph.D

Teknik

Fakultas

Universitas U

ES

ERS AND

nik Mesin

as Teknik

Udayana

2015

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INVERSE MATERIALS PROPERTIES

PREDICTION BASE ON THE VICKERS

AND SPHERICAL INDENTATIONS

OLEH

IR. I NYOMAN BUDIARSA, MT, Ph.D

NIP 196602221991031002

TEKNIK MESIN

FAKULTAS TEKNIK

UNIVERSITAS UDAYANA

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1. Introduction 1

2. Mechanical integrity of welded joints and methods in

characterising material constitutive parameters 3

2.1. Spot Welding Process 3 2.2. Effects of Welding parameters on Weld quality 3 2.3. Typical applications and materials system in resistance

Spot welding. 4 2.4. Microstructure and phase transformations during welding 4

2.5. Mechanical integrity of welded joints 5

2.6. The Materials behaviour of metallic materials and

the properties of different welded zones 6 2.7. Mixed experimental and numerical methods in

characterising material constitutive parameters 12 3. Inverse Materials properties prediction base on the Vickers

and spherical indentations. 20

3.1. Introduction and structure of the research work 20 3.2. FE modelling of the Vickers indentation and

effects of material properties 22

3.3. FE modelling of the Spherical indentation and

Effects of material properties 23

3.4. Method to predict material properties from

the Vickers and Spherical indentation 24

3.4.1. Curvature of the Indentation curve 24

3.4.2. 3-D Mapping approach 25

3.4.3. Dimensional analysis and results 26

3.4.4. Chart based Intersection approach and results 28 4. Mechanical testing and FE Modelling of spot welded Joint 45 4.1.Tensile test of the base material and spot welded joint 45 4.2. Drop mass impact test and results 46 4.3. FE modelling of the spot welded joint (Preliminary results) 47

References 57

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1. Introduction

This report is concerned with a analysis on the development of an inverse/reverse modelling approach to characterise the plastic parameters of elasto plastic materials based on the indentation method and use the approach to measure the properties of resistance spot welded joints with different material systems. Main objective is：

• To develop an reverse/reverse program to predict the materials properties of elasto plastic materials based on the indentation loading curves and conventional static hardness measurements;

• To inversely measure the material properties of the nugget, HAZ and base metal zones using indentation methods;

• To develop numerical models with realistic dimensional data, material properties and correlate the modelling results with experimental test results of static and dynamic deformation;

• To establish the effects of welding parameters on the microstructure (e.g. the dimension of the nugget and heat affected zone (HAZ)) and strength of spot-welded joints of mild steel and stainless steels (dissimilarmaterials).

Progress to date of both experimental and numerical work is reported, which has met the first three main objectives of the project. FE models of sharp indenter (Vickers) and blunt indenter (Spherical indenter) were developed. The effect of some key modelling parameters such as mesh sensitivity, sample size and boundary conditions were assessed. Three reverse/inverse modelling methods (designated as dimensional analysis, 3D mapping and dual indenter chart approach) have been proposed and the validity and accuracy of each approach in predicting the material properties were systematically evaluated using numerical indentation curves. In the experimental part, tensile shear tests have been perform on spot welded joints of different materials. A new drop weight impact testing method has been developed and a detailed analysis approach has been established and validated, before used to analyse the performance of spot welded joints of dissimilar materials.

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2. Mechanical Integrity of Welded Joints and

Methods In Characterising Material Constitutive

Parameters

2.1. Spot Welding Process

In a spot welding process (Fig. 2.1), two or three overlapped or stacked components are welded together as a result of the heat created by the electrical resistance, which is provided by the work- pieces as they are held together under pressure between two electrodes. As shown in the figure, the secondary circuit of a resistance welding machine and the work- piece being welded constitute a series of resistances (Aslanlar S., 2006). The overall resistance also varies with material and the sheet thickness. The force applied to the electrodes assures its continuity. As illustrated in Fig. 2.2, the sequence of operation must first develop sufficient heat to raise a confined volume of metal to the molten state. This metal is then allowed to cool while under pressure until it has adequate strength to hold the parts together. The current density and pressure must be such that a full nugget is formed, but not so high causing molten metal being expelled from the weld zone. In addition, the duration of weld current must be sufficiently short to prevent excessive heating of the electrode faces The welding process is a complex thermal mechanical process and the finished assembly consists of regions with significantly different microstructures and properties, including the base metal, heat affected zone (HAZ) and weld nugget (Fan X.,2007).

2.2. Effects of welding parameters on weld quality

Weld quality depends on process and material variables that affect the heat generation or the electrode pressure, among which, the current, force and time are the three main parameters which determine the strength of the welded joint of a material. The selection of these three parameters is normally determined by generating a weld lobe as shown in Fig. 2.3. The weld lobe curve is a graphical representation of range of welding variables over which acceptable spot welds are formed on a specific material welded with a pre-selected

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electrode force (Aravinthan, 2003). It is determined by making spot welds using different combinations of weld time and welding current. Only welds made with currents and weld times lying within the lobe area are acceptable. Welds made with currents and times exceeding the upper curve experience expulsion; while welds made with currents and times below the lower curve are of insufficient size, or no weld is formed. In both cases, the weld is not acceptable (Aslanlar, et al, 2008).

2.3. Typical applications and materials systems in resistance spot welding

Because of spot welding processes requires relatively simple equipment; it can be easily converted into an automated operation. Once the welding parameters is established, it should be possible to produce repeatable welds. The resistance spot welding is the most widely used joining process for sheet materials. The process is used in preference to mechanical fasteners, such as rivets or screws, when disassembly for maintenance is not required (Chou, 2003). The process is used extensively for joining low carbon steel components for the bodies and chassis of automobiles, trucks, trailers, buses, mobile homes, motor homes and recreational vehicles and roils road passenger cars, as well as cabinets, office furniture, and white-goods manufacturing industries (Hasanbasoglu A., et al, 2007). It is most widely used in joining process for the fabrication of sheet formed components, with or without requirement of special technique (Vural, 2004). Many metallic material such as mild steel, high strength steel, galvanized interstitial free steel, stainless steel, austenitic stainless steel, nickel, aluminium, titanium alloy and brass can be welded by resistance spot welding (Jou M., 2003; Vural M., et al, 2006; Kahraman N., 2007). Small scale resistance spot welding (SSRSW) is also one of the main micro-joining processes being employed in the fabrication of electronic components and devices to joint thin sheet metals of thickness less than 0.2-0.5 mm (Chang B. H., et al, 2003).

2.4 Microstructure and phase transformations during welding

As described in the sections above, spot welding involves thermal, metallurgical and mechanical processes, which result in a structure of mixed phases and properties. Fig. 2.4 shows a typical cross-section of spot welded joint of a low carbon steel (Bayraktar, 2004). There are three main different regions – the base material, the nugget and the heat-affected-zone (HAZ). The block in the centre is the nugget that consists of martensite and

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bainitic phases (Ni K, et al, 2004). The region around the nugget, the so-called heat-affected zone (HAZ), has a mixed microstructure consisting of martensite, bainite, ferrite and pearlite. The nugget is much harder than the base material due to the quenching effect, while the HAZ has a gradient mechanical property and a mixed microstructure with the strength decreasing from the nugget to the base. In many cases, failures of spot welded joints tend to occur around this region, specifically around the heat-affected zone (HAZ) (MukhopadhyayM., 2009).

Many research has been conducted to improve the understanding on spot welded joint as the interactions between electrical, thermal, metallurgical and mechanical phenomena. (Hou Z., et al, 2006). One active research field is on the prediction of the dimension of spot welded joints by simulating the welding process with the finite element modelling (Emmanuel H., et al, 2007; Rahman M. M., et al, 2008). Another active research field is on the study of microstructure development (Sun D.Q., et al, 2007; Bakavos D.,et al, 2010). The microstructure models have to consider the thermo-physical properties of the materials in order to describe the phase transformations during heating and cooling stages (Jou M.,2003, Tan J.C., et al, 2007, Chigurupati P., 2010). These works have resulted in several models to describe the simultaneous formation that has made it possible to predict the microstructure development and transformations during spot welding process, and also to investigate the characteristics and behavior of materials, relating with the applied load conditions on the spot weld joint

2.5. Mechanical integrity of welded joints

Spot welded joints are widely used in many loads bearing situations and their mechanical strength has a strong influence on the integrity of the whole structure. A large amount of research works have been conducted to study the deformation of spot welded joints, experimentally or numerically, under different loading, such as tensile, bending, impact etc. (Darwish, 2003, Cavalli et al, 2003, Yang et al, 2005). Figure 2.5. shows typical mechanical testing methods of spot welded joint, including peel test, lap shear test, cross-tension tests, Impact test, corrosion fatique test, and stress corrosion cracking tests (Alenius, 2006). Each test has its own objectives and the selection of tests hsould be dependent on the service condiiton of the structure being concerned.

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2.6 The materials behaviours of metallic materials and the properties of different welded zones

The plastic behaviour is normally described by the constitutive material equations. In many cases, the three parameter power law hardening rule (Eq. 2.1) is used for steels:

= + ( 2.1) where the parameter ‘

σ

₀_{’ is the yield stress, ‘}_K_{’ is the strength coefficient and ‘}_n’_{is the}

strain hardening exponent. These material parameters influence both the yielding strength and work hardening behaviour of the spot welded joint. The engineering measures of stress and strain, denoted as and respectively, are determined from the measured the load and deflection using the original specimen cross-sectional area and length as

= ; = (2.2) In the elastic portion of the curve, many materials obey Hooke’s law, so that stress is proportional to strain with the constant of proportionality being the modulus of elasticity or Young’s modulus, denoted E:

= (2.3) Using the true stress = P/A rather than the engineering stress = ⁄ can give a more direct measure of the material’s response in the plastic flow range. A measure of strain often used in conjunction with the true stress takes the increment of strain to be the incremental increase in displacement dL divided by the current length L:

= = = ln (2.4) This is called the “true” or “logarithmic” strain. During yield and the plastic-flow regime following yield, the material flows with negligible change in volume; increases in length

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are offset by decreases in cross-sectional area. Prior to necking, when the strain is still uniform along the specimen length, this volume constraint can be written:

= 0 = = (2.5) The ratio is the extension ratio, denoted as λ_{. Using these relations, it is easy to develop}

relations between true and engineering measures of tensile stress and strain

= 1 + = .λ

= ln 1 + = "#λ_(2.6)

These equations can be used to derive the true stress-strain curve from the engineering curve.

The failure of spot welded joints can be overload failure and fracture (Lee H., et al, 2005). Fracture is separation, or fragmentation of a solid body into two or more parts under the action of stress. Fractures of metals are classified two sorts as the fracture behaviour: brittle fracture and ductile fracture. The ductile fracture process in metals usually follows a sequence of three stages: (a) Formation of a free surface at an inclusion or second phase particle by either interface decohesion or particle cracking, (b) Growth of the void around the particle, by means of plastic strain and hydrostatic stress, (c) Coalescence of the growing void with adjacent voids. The linking of voids may occur on planes which are perpendicular to the applied stress (normal rupture), or are parallel to it (delimitation), or along shear bands at angle to it (shear fracture). Most attempts at understanding ductile fracture have considered only the first type. Once a microvoid has been nucleated in a plastically deformed matrix, by either the bending or cracking of a second-phase particles or inclusions, the resulting stress-free surface of the void causes localized stress and strain concentration of the adjacent plastic field. The fracture of spot welded joints is a ductile fracture.

Gurson model is widely used in ductile fracture mechanics, in which, the fracture of material is considered as the result of void growths in the material volume. The Homogenous material surrounding the void is called matrix material. The Gurson model can realistically represent failure, provided the loading state in the coupon used to determine the Gurson parameters, is similar to that in the rupture zone of the structure. The most commonly used model based on the Gurson was called

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Gurson-Tvergaard-Needleman (GTN) model (ABAQUS Theory Manual 6.9), which is briefly described below. The original model developed by Gurson, assumed plastic yielding of a porous ductile material, where the yield surface was a function of a spherical void as follows

$ = %&'(&'(

)*+,) + )- ./01 %*2

)*+, − 4 +

-)_{= 5}_{( 2.7)}

Where ₆ is the yield stress of the material, ₇ is the mean stress, 8 is the void volume fraction. 8 = 0 implies that the material is fully dense, and the Gurson yield condition reduces to that of von Mises; 8 = 1 implies that the material is fully voided and has no stress carrying capacity. 9_:; is the components of stress deviator ( <, > = 1, 2,3 , defined as

&'(= *'(− *2 A'( ( 2.8) And B_:; is the Kronecher delta

A'(= C4 ' = (_{5 ' ≠ (}E

Theoretical micromechanical studies for materials containing periodic distribution of cylindrical or spherical voids have been carried out by Tvergaard (2000). By considering the influence of neighbouring voids on each pair of voids, three parameters, q1, q2, q3, have been added to equation ( 2.9)

$ = %&'(&'(

)*+,) + ) F4 - ./01 % F) *2

) *+, − 4 + F%

-)_{= 5}_{( 2.9)}

G1, G2, G3 are material constants and it was found that matching of test results can be achieved for most alloys, by taking the following material values (ABAQUS Theory Manual 6.4):

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Tvergaard and Needleman have further modified the Gurson model by replacing 8 with an effective void volume fraction, 8∗ 8 :

-∗_{= L}

- '- - ≤ -N

-N+ -PPPPQ-_-O_O_Q-N_N - − -N

-O

PPP '- - ≥ -O

E '- -N < - < -O ( 2.10)

Where :

-O

PPP = F4+ TF4)− F%

The parameter 8_U and 8_V model the material failure due to mechanisms such as micro fracture and void coalescence. 8_U is a critical value of the void volume fraction, and 8_V is the value of void volume fraction at which there is a complete loss stress carrying capacity in the material

The total charge in void volume fraction is given as

-W = -WXY+ -WZ[N\ (2.11)

Where 8W_]^is charge due to growth of existing voids and 8W_{_`U} is change due to nucleation of new voids. Growth of the existing voids is based on the law of conservation of mass and is expressed in terms of the void volume fraction

-XYW = 4 − - aW.b\∶ d

e:; = B:; the unit second order tensor

The nucleation of voids is given by a strain-controlled relationship:

-WZ[N\ = f aPW2b\

Where

f =

-Z

&g√) i

jkl m−

4 )

n

aP₂b\Q ag

o

)

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The normal distribution of the nucleation strain has a mean value _q and standard deviation 9_q, 8_{_} is the volume fraction of the nucleated voids. Gurson model has been implemented in several FE modelling software, like ABAGUS, ADINA, SYSTUS, etc, and is widely used by researchers (ABAQUS Theory Manual 6.9)

Fatigue failure is another problem associated with spot welded joints. Fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The maximum stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material. Some common fatigue mechanisms on metallic material include Time-varying Loading fatigue, Thermal fatigue, Corrosion Fatigue, Surface/Contact Fatigue, combined creep and Fatigue (Matos A., 2010) Time-varying loading fatigue can be defined as a process caused by time-varying load which never reach a high enough level to cause failure in a single application, and yet results in progressive localized permanent damages on the material. The damages, usually cracks, initiate and propagate in regions where the strain is most severe. When the local damages grow out of control, a sudden fracture/rupture ends the service life of the structure. Common categories and approaching methods, include:

The S-N curve Stress Life Method, is the basic method presenting fatigue failure in high cycles (N > 105) which implies the stress level is relatively low and the deformation is in elastic range. Users may check the maximum and minimum stress directly. Define R is the ratio of minimum stress to the maximum stress. Alternatively, define A is the ratio of alternating stress to mean stress.

r = stuv

stwx (2.13)

= sw

st=

zy (2.14)

An approximation based on the zero-mean stress S-N curve proposed by Goodman and Gerber is written as

{ = | }1 − }s_st_~• 6

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Where

| is the stress at fatigue fracture when the material under zero mean stress cycled loading

7 is the mean stress of the actual loading.

` is the tensile strength of the material

R = 1 is called Goodman line which is close to the results of notched specimens.

r = 2 is the Gerber parabola which better represents ductile metals.

Individual contributions, known as Palmgren-Miner's linear damage hypothesis or Miner's rule.

∑

_u •u

qu •u

‚

:ƒ

= „

(2.16) Where

k is the total number of different stress magnitudes in a spectrum

9:(1≤ < ≤ …) is the magnitudes of each different stress in sprectrum

#: 9: is the actual number of cycle under the specific stress 9:

†: 9: is the total number of cycle to failure under the specific stress 9_: 0.7 < c < 2.2 is an material dependent constant obtained by experiments.

Set c = 1, if there is no further information available

Derived relationship for the stage II crack growth with cycle N, in term of the cyclical component ∆_{K of the stress intensity factor K}

{

= ‡ ∆

7 (2.17)

Where ‰ †⁄ is the crack length and m is typically in the range 3 to 5 (for metal)

The impact strength of spot welds is a very important quality index in the automotive industry, impact test conducted to determine the impact energy & Impact performance of weld through impact process characteristics such as impact force and displacement profiles (Zhang H., et al, 2001). Impact tests were also performed to evaluate of resistance to dynamic failure in the characteristics and behaviour of thin welds of different grades of steels in dynamic loading conditions (Bayraktar E., 2004). The absorbed energy is

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determined by integration of the force vs. deformation curve. The mean crush load for a given deformation is defined as the absorbed energy divided by the deformation

The energy absorbed by the specimen during crushing, EA, is equal to the area beneath the load vs. displacement curve and can be defined as follows (Joosten M.W., 2010):

EA =

"

(2.18) where " is the stroke or displacement of the crosshead and is the applied axial force. The specific energy absorption, SEA, is defined as the energy absorbed per unit mass of destroyed structure and can be defined as follows:

SEA = _{9‘•’„‘’•Ž “Ž<•ℎ‘}Š‹Œ•ŠŽ #Ž•••

SEA = •–

—

(2.19)

which is a function of the density, ˜, the cross sectional area of the structure, A, and the absorbed energy, EA, over a crushing stroke, ". Note that the cross sectional area in the steeple trigger zone is not constant, and is calculated as a function of the axial displacement,".

On axial crushing test with high speed crushing, the value of impact energy similar with that given in eq.2.20

EA = _I › œI _(2.20)

Where m is the mass of the crosshead and v the crush velocity

2.7. Mixed experimental and numerical methods in characterising material constitutive parameters

The elastic-plastic material parameters and the fracture parameters of materials can be readily determined when standard specimens are available. However, for a spot welded joint, standard testing is not applicable to characterise the HAZ and nugget due to their complex structure and small size. One potential approach to be developed in this work is

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to use a mixed experimental-numerical method based on the indentation test to inversely characterise the parameters of the constitutive material laws for the nugget, HAZ and the base. In a mixed numerical-experimental approach, the load-deformation data of the material is used as input data to a finite element (FE) model that simulate the geometry and boundary conditions of the experiment. This approach has been used on some non-standard specimens or surface loading situations, such as in vivo (within a living organism) tension, indentation, etc. (Meuwissen et al, 1998, Shan et al, 2003; Gu et al, 2003; Bolzon et al, 2004, Ren et al, 2006). With indentation tests, the local plastic properties can be calculated by solving the inverse problem via finite element analysis by incrementally varying properties in 3D modeling to find a similar simulated load– displacement curve as compared with experimental one.

Fig. 2.1 The setup of a spot welding system and the resistances occurring in the welding

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Fig. 2.2 Basic welding cycle(s) for spot welding (Aslanlar S., 2006).

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(a) Different structure zone of steel weldment (Bayraktar E., 2004)

(b) Typical structure of welded joint of dissimilar materials, A- Asymmetric penetration in the dissimilar metal joint of EN 1.4318 2B and ZStE260BH steels; B - dissimilar metal joint of EN 1.4318 2H and DX54DZ steels (Alenius, 2006)

Fig. 2.4 Different structure zones of welded joints.

Base Nugget Heat affected zone

(HAZ)

Grain

growth zone

Recrysatllised

zone

Partial

transformed zone

Tempered

zone

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Testing Methods Specimen Peel test.

Lap shear test.

Cross tension test.

Impact test.

fatigue test

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(a)Different types of indenters

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Figure. 2.6 (a) Different indenter types; (b) Schematic illustration of a typical P-h response of an elasto plastic material to sharp indentation

P = C (P)

Load

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Fig. 2.7 Parametric modelling approach to extract the material properties(Ren et al 2006).

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3. Inverse Material Properties Prediction Base On

The Vickers And Spherical Indentations

3.1. Introduction and structure of the research work

The deformation of spot welded joints is challenging research problem due to the complex nature of the structure. One major problem is to characterise the materials properties. The elastic-plastic material parameters and the fracture parameters of materials can be readily determined when standard specimens are available. However, for a spot welded joint, standard testing is not applicable to characterize the HAZ and nugget due to their complex structure and small size. In an previous work, an parametric based approach has been developed, which determine the material parameters by cross compare an indentation curve with numerical curves for all the materials properties over a wide spectrum, then using the objective functions the mean to determine the final optimum data (Kong, 2008). This has opened up the possibility to characterize the material properties based a dual indenter method. However, the method involved intensive data fitting which has to be performed based on a computational program. This work aims to further develop this method based to enable more direct parameter prediction based on analytical or semi-analytical approaches with either continuous indentation loading curve or conventional hardness tests. The approach will then be used to test different welding zones and the material parameters thus predicted used to simulate the deformation of spot welded joints under complex loading conditions including tensile shear and drop weight impact tests.

Figure 3.1 shows the work plan of the project. In the first stage FE models of sharp indenter (Vickers) and blunt indenter (Spherical indenter) were developed. The effect of some key modelling parameters such as mesh sensitivity, sample size and boundary conditions were assessed. The accuracy of the Vickers indentation was validated by comparing the modelling results with published data. In the next stage, the effect of the key material properties including the work hardening coefficient and the yield strength were established. Three reverse/inverse modelling methods (designated as dimensional

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analysis, 3D mapping and dual indenter chart approach) have been proposed and the validity and accuracy of each approach in predicting the material properties were systematically evaluated using numerical indentation curves. In the experimental part, tensile shear tests have been perform on spot welded joints of different materials. A new drop weight impact testing method has been developed and a detailed analysis approach has been developed and validated, before used to analyse the performance of spot welded joints of dissimilar materials In the next stage, the inverse material properties approach is to be extended to conventional hardness tests to characterise the properties of different structure zones within the welded joints. The properties predicted will then be used to develop a numerical model with realistic material poverties to simulate the deformation of the joint under different loading conditions.

Commercial finite element analysis (FEA) software package ABAQUS version 6.9.1 is used in the numerical simulation. The elastic-plastic materials behaviours were represented, respectively, by Hooke’s law and Von Misses yield criterion with isotropic power law hardening. In the models, the true stress-strain behaviour of the materials following constitutive law

= •

_r

8Œ• ≤

_{8Œ• >}

E

(3.1)

Where is the Young’s modulus, r a strength coefficient, n the strain hardening exponent and ₆ the initial yield stress at zero offset strain. In the plastic region, true strain can be decomposed to strain at yield and true plastic strain

=

+

(3.2)

For continuity at yielding, the following condition must hold ( = ₆ )

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If the yield stress ( ₆) is defined at zero offset strain. Hence the true stress-true strain behaviour is written to be (Swaddiwudhipong et al, 2005):

=

,

n

_s¡_¢

o

E

(3.4)

In these indentation FE models, the Young’s modulus ‘E’ of the work piece materials was set to 200 GPa and Poisson’s ratio was set to 0.3, which were commonly used value for steel (Chen et al, 2007).

3.2. FE modelling of the Vickers indentation and effects of material properties

Figure 3.2.(a) show the FE Models of the Vickers indentation. Only a quarter of the indenter and material column was simulated as a result of plan symmetric geometry. The sample size is more than 10 time the maximum indentation depth, which is sufficiently large to avoid any sample size effect or boundary effect (Johnson, 1985). The bottom face of the material volume was fixed in all degrees of freedom (DOF) and two side faces (A and B) were symmetrically fixed in z and x direction. The element type used is C3D8R (reduced integration element used in stress/displacement analysis). Contact was defined at indenter facet. The material of interest was allowed to move and the contact between the indenter surface and the material was maintained at all the time. The mesh in the regions with large deformation such as that directly under the indenter tip was refined with high mesh density in order to obtain more accurate results.

The Vickers indenter has the form of the right pyramid with a square base and an angle of

136 between opposite face. It is normally made of diamond with Young’s modulus of over 1000 GPa, which is significantly stiffer than steel (E=200 GPa). The indenter was considered as the rigid body to improve the modelling efficiency. A predefined displacement was applied in a ramp mode and the reaction force is recorded on the reference point, representing the overall load on the indenter. Figure 3.2 (b) shows a typical P-h curve (Force Vs Indentation depth) during loading and unloading phase ( ₆ =100 MPa, n=0,01). The loading curve represents the resistance of material to indenter

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penetration, while difference between the loading and loading curve represents the energy loss (Swaddiudhipong et al, 2005). The unloading part of the P-h curve is primarily influenced by E, as it is essentially an elastic process, while the loading part of the P-h curve correlates with ₆ and n (Taljat, 1998). This work is focused on the studies of plastic parameters, so only the loading curve was utilised to predict the plastic material parameters. Figure 3.3 (b) illustrated the effect of material properties on the P-h curves of Vickers indentation ( ₆ =300 MPa) with E set at 200 GPa for Steel. It is clearly shown that both the yield strength and work hardening coefficient influence the indentation curves.

3.3. FE modelling of the spherical Indentation and effects of material properties

Different from the Vickers indenters, spherical indenter is fully asymmetric, a typical FE model is shown in Figure.3.4.(a). A planar specimen (3X3››I) has been used and this specimen size is large enough to avoid potential sample size effect. The movement of the indenter was simulated by displacing a rigid arc (rigid body) along the Z axis. The bottom line was fixed in all degree of freedoms (DOF) and the central line was symmetrically constrained. The element types used in the spherical indentation model are CAX4R and CAX3 (4-node bilinear asymmetric quadrilateral and 3-node linear asymmetric triangle element used in stress/ displacement analysis without twist).

A gradient meshing scheme has been developed for different regions. The mesh size is 5¤m in the region underneath and around the indenter as shown in Figure 3.4.(b), while the mesh size of other regions from the nearest region to the outer edge varied from 10 ¤m, 0.05 mm and 0.1mm; the mesh of the transitional regions is mainly triangle element following a free meshing scheme. Figure 3.4 (c) shows a typical numerical force indentation depth curve (loading and unloading curves) of a spherical indenter (R= 0.5mm

6= 500, n=0.024). The curve is significantly different from Vickers with much higher forces due to the larger contact area in a spherical indentation. Figure 3.5 illustrate the effect of plastic material properties on the P-h curves of the Spherical indentation. It clearly shows that both the yield stress and work hardening coefficient influence the results.

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3.4. Method to predict material properties from the Vickers and spherical indentation

3.4.1. Curvature of the indentation curve

As shown in Figures 3.3-5, the P-h curves for both Vickers and Spherical indentation obtained the following relationship:

C =P ℎ⁄ I (3.5) Where P and are the load and indentation depth on the loading curve respectively. C is the curvature coefficient with the curvature for the Vickers Indentation and spherical indenter designated as ‡_¦ and ‡_§ respectively. The curvature is a function of the yields stress and the work hardening coefficient. This will provide a relationship which potential allow the prediction of material parameters from continuous indentation tests.

Figure 3.6 is a flow chart showing the main structure of the inverse modelling approach to predict the material properties. In the first stage, systemic FE models were developed to form he simulation space covers the potential range of material properties. In the next stage, the loading curves were used to develop an simulation space. The data will then be processed through three different approaches (3D mapping, dimensional analyse, and dual indenter chart approach) to predict the material parameters. Details of each approach and the results were presented in the next sections with discussion.

The three approaches have been comparative developed to assess their suitability to predict the materials properties based on the dual indenter approach. The second approach is normalised dimensionless analysis in which the relationship is normalised than a dimensionless analysis is applied. In the third approach, the relationship between the curvature for both the Vickers and spherical were developed then used a chart to predict all the material sets with the same curvature. The relationship is used to predict the material sets have the sane indentation curvature. The key procedures of each approach and the typical results are detailed in the next three sections.

3.4.2. 3D- Mapping approach

In the 3D mapping approach, the curvature data were plotted against the materials properties, the an equation is developed base on either linear or nonlinear fitting, which will give an equation between curvature and working hardening and yield stress. Variations of the curvature (Cv and Cs) with respect to ₆ and n for Vickers indenter were

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illustrated by the surface show Figure 3.7. The data for construction of these surfaces were obtained numerically through indentation finite element analysis encompassing a domain of ₆ from 100 to 190MPa and n varying from 0.01 to 0.5 It clearly showed that the curvature coefficients increased with ₆ and n but with different gradients for different regions.

The evaluation performed on surface plot 3D of loading curvature and properties material, this approach was started by setting the value of curvature and properties material as mapping 3D. A linear fitting plane is shown in Figure 3.7(a) & (b). For each curvature value, there are an array of material property sets. These data were extracted and plotted in Figure 3.7 (c). The material property set at the intersection point between the data for the Vickers and Spherical indentation will represent the true material properties. The accuracy of the approach has been assessed using a range of initial values, the results were listed din Table 3.1. Similar approach has been applied to the data using Nonlinear (Parabolic) mapping and the results were shown in Figure 3.8 (a)(b) and the results of the accuracy test was listed in Table 3.2.

Evaluation of accuracy on the approach using 3D chat mapping carry out by taking input data which is characterized by randomize and represent the sample space. The selected input data with 2 variations in the value (n), namely n=0.15 and n=0.28 (range 0.01 0.30) and ₆ = 100, 140, 190 and 300. Accuracy study chat mapping 3D-Linier (Table.3.1), known that on average value of different predictive of (n) into n-input as n=0.056 0.069 and average accuracy error ∆n n⁄ (%) is 0.1% both the prediction (n) on Vickers Indentation and on Spherical Indentation. This shows the selected predictors significantly acceptable within the limit of level confidence less than 0.5 %. While on an Accuracy study chat mapping 3D-Non Linier (parabolic) (Table.3.2.), known that on average value of different predictive of (n) into n-input as n=0.059 0.061 and average accuracy error

∆n n⁄ (%) is 0.22% both the prediction (n) on Vickers Indentation and on Spherical Indentation. This shows the selected predictors significantly acceptable within the limit of level confidence less than 0.5 %. By Comparing the two approaches chat mapping 3D, known to have smaller average error by prediction using mapping 3D linear ∆n n⁄ (%) is 0.1% compared using the non linear (parabolic) ∆n n⁄ (%) is 0.22%. This evaluation showed that the 3D chat mapping approach can serve as predictor value work hardening coefficient (n) of both the prediction (n) on Vickers Indentation and on Spherical Indentation

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3.4.3. Dimensional analysis and results

In the dimensional analysis, an relationship between the curvature the material properties were developed based on the dimensional analysis. Dimensional analysis has proven to be useful to the study of the contact mechanics for instrumented normal indentation (Cheng.

et al, 2004). In Indentation, indenting normally into a power law elasto plastic solid, the

load P can be written as (Dao, 2001).

P = P h, E, v, Eª, vª, σ¬, n (3.6)

Where E_ª is Young’s modulus of the indenter, and v_ª is its Poisson’s ratio. By combining elasticity effects of an elastic indenter and an elasto plastic solid as

P = P h, E∗_{, σ}

¬, n (3.7)

Where

E

∗

_{= }}

Q-®

•

+

Q-u®

•u

•

(3.8)

Alternatively, equation (3.7) can be written as

P = P h, E∗_{, σ}

¯, n (3.9) Or

P = P h, E∗_{, σ}

¬, σ¯ (3.10)

Applying the theorem in dimensional analysis, equation (3.9) becomes

P = σ° hI ∏ 1 • ∗

²³, n (3.11)

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C = _¶µ®= σ¯∏ 1 ·• ∗

²³, n¸ (3.12)

Where ∏ 1 is a dimensionless function. similarly, applying the theorem to equation (3.10), loading curvature C may alternatively be expressed as

C = _¶µ®= σ¬ ∏ 1 n• ∗ ²¹ ,

²³

²¹o (3.13)

Where ∏ 1 is a dimensionless function, the dimensionless given in equation (3.12). and the normalization was taken with respect to E∗ instead of ₆ or _^

Figure 3.9.(a) shows the relationship between normalised Cv Vs properties material, and Figure 3.9.(b). Show the relationship between normalized Cs Vs properties material (strain hardening exponent (n) and Yielding stress). It is clearly shown that all the data. Curve fitting has been performed by iterating the relationship between loading curvature indentation and properties material ( ₆, # as following equations

C

=

6J º⁄

374.14 Ž

J. ½¾ _

(3.14) Similarly an equation has been determined for the Spherical indentation

C

=

6J º⁄

8011.9 Ž

.½Âº _ (3.15) Using the relationship determined, for each combination of Cv and Cs, there are a range of material data as shown in Figure 3.9.(c). The intersection point will represent the predicted material properties. In this case, for ₆= 150, n=0.2, Cv = 30647.664 and Cs = 515752. The predicted value are ′₆= 149, n’ =0.209.Accuracy studies results were done for some input value, the results were listed in Table 3.3. The average accuracy error ∆ _{6 / 6} = 0.065196 and n/n = -0.06296, which is much better than the accuracy for the 3D mapping approach.

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3.4.4. Chart based Intersection approach and results

In the chart based intersection approach, the potential material sets with the same curvature value for the Vickers and spherical indenters were identify separately through a chart (C vs. N) for different yield stress (Figure 3.10 (a) & (b)). The property data was then plotted onto another chart for yield stress vs. Work hardening coefficient (Figure 3.10 c). The properties were determined at the intersection point between the data for the Vickers and Spherical indenters. As illustrated in Figure 3.10 (a), (b), (c) with a known Cv or Cs value, the properties can be determined by drawing a straight line along the curvature value, the intersection point represents data with the same curvature value. These data was then plotted onto the yield stress-work hardening n chart. The intersection point will represent the predicted material properties. The two cases represents two examples for ( ₆1= 150, n1=0.15) and ( ₆2= 300, n2=0.28), both are very close to the true material properties. Prediction carry out by determining the value of n (work hardening coefficient) based on analysis of trend equations at each curvature Through chat fitting and mapping knowable predicted value n1 = 0.174 , n2 =0.209 as described on accuracy study results of inverse FE modeling on Vickers and spherical indentation plotting and mapping data result. Evaluation of accuracy on the approach using Plotting and mapping carry out by taking input data which is characterized by randomize and represent the sample space. The selected input data with 2 variations in the value (n), namely n=0.15 and n=0.28 (range 0.01 0.30) and ₆ = 100, 140, 190 and 300. Accuracy study Plotting and mapping (Table.3.4), known that on average value of different predictive of (n) into n-input as n=0.24 and average accuracy error ∆n n⁄ (%) is 0.07% both the prediction (n) on Vickers Indentation and on Spherical Indentation. This shows the selected predictors significantly acceptable within the limit of level confidence less than 0.5 %.Accuracy studies results were done for some input value, the results were listed in Table 3.4. The average accuracy, which is much better than the accuracy for the 3D mapping approach.

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Figure 3.1 Flow chart showing the Research work. Development of FE indentation models of Vickers and Spherical indenters

Validation of the FE model and the effect of materials properties on the loading and unloading curves.

Theoretical development of the inverse FE modelling program based on indentation curves with different indenter shapes: Curve fitting; 3-D Mapping, Chart method.

Evolution of accuracy of each approach with known material properties

Tensile shear tests of spot welded joints Impact tests of spot welded joints

Development of analysis procedures for drop weight impact testing of spot welded joints

Develop a practical approach based conventional hardness testing (measurement after unloading)

Development of FE models of spot welded joints with realistic structures under tensile shear

Prediction of the behaviour of spot welded joint with realistic materials properties

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(a)

(b)

Figure 3.2 (a) FE model of the Vickers Indentation test; (b) Typical force- Indentation depth (P-h) curve during loading and unloading of the Vickers indentation ( ₆= 100 MPa, n= 0.01)

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

0 0.005 0.01 0.015

(

)

h(mm)

A B

136 between

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(a) Effect of the yielding strength

(b) Effect of work hardening coefficient.

Figure 3.3 Effect of work hardening and yield strength on the P-h curves of the Vickers indentation.

0 1 2 3 4 5 6 7

0 0.005 0.01 0.015

Sy=100, n=0.2 Sy=120, n=0.2 Sy=150, n=0.2 Sy=190, n=0.2 Sy=300, n=0.2 Sy=390, n=0.2

0.000E+00 1.000E+00 2.000E+00 3.000E+00 4.000E+00 5.000E+00 6.000E+00 7.000E+00

0.000E+00 5.000E-03 1.000E-02

Sy 300, n=0.01 Sy 300, n=0.1 Sy 300, n=0.2 Sy 300, n=0.3

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(a) FE model of the Spherical (b).Close-up view showing the Indentation test the mesh underneath the indenter

Figure.3.4(a), (b) FE models of the Spherical Indentation test (R=0.5mm).

(c)

Figure.3.4.(c). Typical force-indentation depth (p-h) curve during loading and unloading for Spherical Indentation ( ₆= 500 MPa, n=0.024).

0 20 40 60 80 100 120 140

0 0.005 0.01 0.015 0.02 0.025

(

)

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Figure 3.5 (a) Effect of yield stress ( ₆) as plastic parameter on the p-h curves of the spherical Indentation.

Figure 3.5 (b)Effect of Work hardening coefficient (n) as a plastic parameter on the P-h curves of the spherical indentation

0 20 40 60 80 100

0 0.005 0.01 0.015 0.02 0.025

(

)

h (mm)

SY=100 n= 0.01 SY=200 n=0.01 SY=300 n=0.01 SY=400 n=0.01 SY=500 n=0.01

0.000E+00 5.000E+00 1.000E+01 1.500E+01 2.000E+01 2.500E+01 3.000E+01 3.500E+01 4.000E+01 4.500E+01 5.000E+01

0.000E+00 5.000E-03 1.000E-02

Sy 200, n=0.01 Sy 200, n=0.1 Sy 200, n=0.2 Sy 200, n=0.3

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Input experimental Force Vs depth data

Simulation Space

Figure 3.6. Flow chart showing the inverse FE modelling approach based on the Vickers and Spherical Indentation tests.

0 50 100

0 0.01 0.02 0.03

P ( N ) h (mm) 0 20 40 60 80 100

0 0.02 0.04

(

)

h (mm)

0 1000 2000 3000 4000

0 1 2 3

S tr e ss , M p a Strain

Three inverse properties prediction methods:

• _{Dimensional analysis}

approach

• 3D mapping approach • Dual indenter Chart based

*

and n

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Figure 3.7 (a).Surface mapping (linear fitting) plot of loading curvature vs material properties.

Figure 3.7 (b). Typical materials parameter prediction process based on linear 3-D mapping method -3.00E-01 -2.00E-01 -1.00E-01 0.00E+00 1.00E-01 2.00E-01 3.00E-01 4.00E-01 5.00E-01 6.00E-01 7.00E-01

0 50 100 150 200 250 300 350

Yield Stress, Mpa

Cv 150 Cs 150 Cv 300 Cs 300 0.0 2.0e+5 4.0e+5 6.0e+5 8.0e+5 1.0e+6 1.2e+6 100 120 140 160 180 0.1 0.2 0.3 0.4 C s Sy n

3D Linear mapping

0 2e+4 4e+4 6e+4 8e+4 1e+5 100 120 140 160 180 0.1 0.2 0.3 0.4 C v SY n

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Accuracy study

Input data Vickers Indentation + Spherical indentation

Material properties Value curvature Predicted value

Different with input value

Accuracy (error %)

Predicted value

Different with input

value

Accuracy (error %)

n *₊ Cv Cs n ∆n ∆n/n n ∆n ∆n/n

0.15 100 26008 466275 _2.052E-01 _5.523E-02 _3.682E-01 _2.477E-01 _9.770E-02 _6.513E-01

0.15 140 26008 466275 _1.538E-01 _3.786E-03 _2.524E-02 _1.639E-01 _1.388E-02 _9.253E-02

0.15 190 26008 466275 _8.949E-02 _-6.051E-02 _-4.034E-01 _5.911E-02 _-9.089E-02 _-6.059E-01

0.15 300 26008 466275 _-5.198E-02 _-2.020E-01 _-1.347E+00 _-1.714E-01 _-3.214E-01 _-2.143E+00

0.28 100 61940 925826 _5.749E-01 _2.949E-01 _1.053E+00 _6.391E-01 _3.591E-01 _1.283E+00

0.28 140 61940 925826 _5.235E-01 _2.435E-01 _8.695E-01 _5.553E-01 _2.753E-01 _9.833E-01

0.28 190 61940 925826 _4.592E-01 _1.792E-01 _6.398E-01 _4.506E-01 _1.706E-01 _6.091E-01

0.28 300 61940 925826 _3.177E-01 _3.770E-02 _1.346E-01 _2.201E-01 _-5.994E-02 _-2.141E-01

Table 3.1. Accuracy study results of inverse FE modelling on Vickers and Spherical indentation by 3D Linier Predicted chart mapping

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Figure 3.8 (a).Surface mapping (nonlinear fitting) plot of loading curvature vs

material properties.

Figure 3.8 (b) Typical materials parameter prediction process based on nonlinear 3-D mapping method. -6.00E-01 -4.00E-01 -2.00E-01 0.00E+00 2.00E-01 4.00E-01 6.00E-01 8.00E-01

0 100 200 300 400

Yield Stress, Mpa

Cv 150 Cv 300 Cs 150 Cs 300 Cs 180 0 2e+4 4e+4 6e+4 8e+4 1e+5 100 120 140 160 180 0.1 0.2 0.3 0.4 C v Sy n 0.0 2.0e+5 4.0e+5 6.0e+5 8.0e+5 1.0e+6 1.2e+6 120 140 160 180 0.1 0.2 0.3 0.4 C s Sy n 3D Non linear

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Table 3.2. Accuracy study results of inverse FE modelling on Vickers and Spherical indentation by 3D Non Linier (Parabolic ) Predicted chart mapping

Accuracy study

Input data Vickers Indentation- Spherical indentation

Material properties Value curvature Predicted value

Different with input value

Accuracy (error %)

Predicted value

Different with input

value

Accuracy (error %)

Sy n *₊ Cv Cs n ∆n ∆n/n n ∆n ∆n/n

150 0.15 100 26008 466275 _0.230977 _8.098E-02 _5.398E-01 _0.270383 _1.204E-01 _8.026E-01

150 0.15 140 26008 466275 _0.166904 _1.690E-02 _1.127E-01 _0.175556 _2.556E-02 _1.704E-01

150 0.15 190 26008 466275 _0.077722 _-7.228E-02 _-4.819E-01 _0.034696 _-1.153E-01 _-7.687E-01

150 0.15 300 26008 466275 _- _- _- _- _- _-

300 0.28 100 61940 925826 _0.490031 _2.100E-01 _7.501E-01 _0.562677 _2.827E-01 _1.010E+00

300 0.28 140 61940 925826 _0.454171 _1.742E-01 _6.220E-01 _0.505893 _2.259E-01 _8.068E-01

300 0.28 190 61940 925826 _0.412688 _1.327E-01 _4.739E-01 _0.43741 _1.574E-01 _5.622E-01

300 0.28 300 61940 925826 _0.33883 _5.883E-02 _2.101E-01 _0.301386 _2.139E-02 _7.638E-02

180 0.25 100 61940 925826 _0.354054 _1.041E-01 _4.162E-01 _0.399732 _1.497E-01 _5.989E-01

180 0.25 140 61940 925826 _0.30762 _5.762E-02 _2.305E-01 _0.326902 _7.690E-02 _3.076E-01

180 0.25 190 61940 925826 _0.251198 _1.198E-03 _4.792E-03 _0.233276 _-1.672E-02 _-6.689E-02

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Figure 3.9(a) Effects of Yield strength ( ₆) on the value loading curvature (Cv) and work hardening coefficient (n) on Vickers Indentation.

Figure 3.9 (b) Effects of Yield strength ( ₆) on the value loading curvature (Cs) and work hardening coefficient (n) on Spherical Indentation

y = 374.1e3.196x

0 200 400 600 800 1000 1200 1400 1600

0.000 0.100 0.200 0.300 0.400 0.500

C v /s y ^ 3 /4 n Sy=100 Sy=120 Sy=150 Sy=190 Sy=300 Prediction Cv Expon. (Prediction Cv)

y = 8011.e1.983x

0 5000 10000 15000 20000 25000 30000 35000

0 0.2 0.4 0.6 0.8

C s/ S y ^ 3 /4 n Sy=100 Sy=120 Sy=140 Sy=190 Sy=300 prediction Cs Expon. (prediction Cs)

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Figure 3.9(c). Typical materials parameter prediction process based on the intersection between properties line for the Vickers and Spherical indentation ( ₆= 120 Mpa, n=0.2).

0.000000E+00 5.000000E+01 1.000000E+02 1.500000E+02 2.000000E+02 2.500000E+02 3.000000E+02

0 0.1 0.2 0.3 0.4 0.5 0.6

(

)

Work Hardening coefficient (n)

Sy(n,Cv) Sy(n,Cs) 1.200E+02

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Input data Accuracy study

Material properties Value of Curvature Predicted values Differences with input value Accuracy (error%)

σ_y n Cs Cv σ_y n ∆σ_y ∆n ∆σ_y / σ_y ∆n/n

100 0.1 303841.62 15725.77 102 0.09 -2 0.010 -0.020 0.10000

100 0.2 387159.42 22631.67 105 0.19 -5 0.010 -0.050 0.05000

100 0.3 495483.94 32535.09 111 0.29 -11 0.010 -0.110 0.03333

200 0.1 5.260E05 2.771E+04 202 0.09 -2 0.010 -0.010 0.10000

200 0.2 6.297E05 3.767E+04 195 0.21 5 -0.010 0.025 -0.05000

200 0.3 7.547E05 5.061E+04 195 0.31 5 -0.010 0.025 -0.03333

290 0.1 6.892E05 3.734E+04 275 0.12 15 -0.020 0.052 -0.20000

290 0.2 8.039E05 4.885E+04 265 0.22 25 -0.020 0.086 -0.10000

290 0.3 9.365E05 6.349E+04 255 0.31 35 -0.010 0.121 -0.03333

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Figure 3.10 (a) Typical curves of the Cv vs. n for Vickers indentation and the interception line to identified the material parameters with identical Cv value.

(b)

Figure.3.10 (b) Typical curves of the Cs vs. n for Spherical indentation and the interception line to identified the material parameters with identical Cs value.

y = 14834e3.353x

y = 11002e3.608x

y = 19655e3.061x

y = 29685e2.614x

0 10000 20000 30000 40000 50000 60000 70000

0 0.1 0.2 0.3 0.4

C v n Sy=140 Sy=100 sy=190 Sy=300 Expon. (Sy=140) Expon. (Sy=100) Expon. (sy=190) Expon. (Sy=300) 26008

y = 23802e2.447x

R² = 1

y = 42235e1.818x

R² = 0.999 y = 32353e2.098x

R² = 1 y = 61251e1.448x

R² = 0.999

0.000000E+00 2.000000E+05 4.000000E+05 6.000000E+05 8.000000E+05 1.000000E+06 1.200000E+06 1.400000E+06

0 0.2 0.4 0.6

C s n sy=100 sy=190 sy=140 sy=300 Expon. (sy=100) Expon. (sy=190) Expon. (sy=140) Expon. (sy=300 ) 466275

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Figure 3.10 (c). Typical materials parameter prediction process based on dual indenter chart method.

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

0 50 100 150 200 250 300 350

Yield Stress, Mpa

Cv(150, 0.15) Cs(150, 0.15) Cv(300, 0.28) Cs(300, 0.28)

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Table.3.4. Accuracy study results of inverse FE modelling on Vickers and Spherical indentation by Plotting and mapping data result from Cv and Cs chart to used predicted materials

Accuracy study

Input data Vickers Indentation

Spherical indentation Material properties Value curvature Predicted

value

Different with input value

Accuracy (error %)

Predicted value

Different with input value

Accuracy (error %)

n *₊ Cv Cs n ∆n ∆n/n n ∆n ∆n/n

0.15 100 26008 466275 0.23831 8.832E-02 5.888E-01 0.274451 1.245E-01 8.297E-01

0.15 140 26008 466275 0.167607 1.761E-02 1.174E-01 0.174204 2.420E-02 1.614E-01

0.15 190 26008 466275 0.091527 -5847E-02 -3.898E-01 0.083707 -6.629E-02 -44.420E-01

0.15 300 26008 466275 -0.05067 -2.007E-01 -1.338E+00 -0.18814 -3.381E-01 -2.254E+00

0.28 100 61940 925826 0.478695 1.987E+01 7.096E-01 0.554414 2.744E-01 9.801E-01

0.28 140 61940 925826 0.42664 1.466E-01 5.237E-01 0.50114 2.211E-01 7.898E-01

0.28 190 61940 925826 0.375109 9.511E-02 3.397E-01 0.45000 1.700E-01 6.071E-01

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4. Mechanical testing and FE Modelling of spot

welded Joint

4.1. Tensile test of the base material and spot welded Joint

Tensile-Shear test of spot weld joint has objectives for determining the elastic plastic behaviours of the welded joints being tested. Two specimen with different materials (stainless steel and Mild steel) and thickness were used. The chemical composition of two base steel are listed in Table 4.1. Stainless steel used is stainless steel grade 304 with a width of 25mm, and thickness of 0.8mm, the other specimen is mild steel with a width of 25mm and thickness of 1.44mm. Spot welded joint of two material combinations have been prepared and tested. The first one is stainless steel to stainless steel; while the other one is stainless steel to mild steel. Tensile tests were performed using a Lloyd LR 30K Universal material testing machine which can perform both tensile and compression tests. The machine has a maximum loading capacity of 30kN, with the readings being accurate to 0.5% of the force. The Lloyd is interfaced with a microcomputer so graphical printout of the tests can be obtained and test data saved. The control console of the testing machine has a digital display where the machine can be operated either manually or remotely. The test-piece is loaded into position and the jaws tightened with a pre-load of approximately 50 N. In the test the specimen was clamped with two gaskets to avoid the bending during test. The tensile test was performed at a loading rate 5 mm/minute. Typical testing data was shown in Figure 4.1. The initial elastic loading part is comparable between these two specimens, but the yielding point and the plastic deformation part is significantly different, with the SS-MS specimen much stronger than the SS-SS specimen.

Table 4.1. Chemical Composition material spot weld joint

Concentration C Cr Ni Mn Si P S

Stainless steel G304

<0.08% 17.5-20% 8-11% <2% <1% <0.045% <0.03%

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4.2. Drop mass impact tests and results

Drop mass tests were performed in order to determine the effect of materials on deformation of welded joints under dynamic loading, which represents the crash and energy absorption characteristics of structure. The method utilises a drop mass impact configuration with mass and impact velocity selected such that the crush speed remains approximately uniform during the entire sample crushing event. Figure 4.2 (a) shows the setup of the machine. In the test, single accelerometer is mounted on the drop mass. Drop mass including the flat platen is 0.6 Kg, the maximum distance of drop is 75 cm. Measurement accuracy is maintained with regarding to the crushable foundation, which remains undeformed (rigid Flat) while the sample undergoes crushing. The relative acceleration between the drop mass and foundation was measured by connecting the pulse of the acceleration displayed from accelerometer as gravitational acceleration (Gravitational acceleration is the acceleration caused by the gravitational attraction of massive bodies in drop mass) to the recording devices, then the pulse is amplified that record the acceleration data as a function of time. The crush load is determined by the measured deceleration multiplied by the magnitude of the drop mass. The impact velocity is measured by the integration of the acceleration of the drop head, and the crush displacement is measured by the double integration of the deceleration/time history. Typical deformed specimen of three material combinations were shown in Figure 4.2(b). As shown in the figures, the deformation mode of the three spot welded joints made of different material systems are significantly different. To quantify the difference, the acceleration time data need to processed following the procedure listed in Figure 4.3. The procedure was adapted from the method used to analysis the data from crush testing using guided drop mass impact on foams (NASA,Kellas S.,2004). As illustrated in Figure 4.4, in this process, raw data was processed to remove mechanical vibrations, as well as electrical noise. Consequently, filtering and other extensive data processing is necessary to isolate useful mechanical properties from the experimental data. Because the data must be filtered, the sampling rates have to be chosen in such a way that useful signal information is not lost. As shown in Figure 4.4, the analysis process of the foam tests data involves initial identification of important events then the acceleration was processed into velocity, which in turn can be used to determine the displacement and stress strain data (if the loading area is known). The final results shown in Figure 4.4 was comparable to the published data, this validated the procedures before it was used to process the testing data

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on spot welded joints. Figure 4.5 shows the acceleration vs time data, while the predicted displacement vs. Time data was shown in Figure 4.6. The results clearly show that the dynamic behaviour of the spot welded joints with different material systems is significantly different. These data are to be used in future works to validate the FE model which is briefly described in the next section.

4.3. FE modelling of the spot welded joint (Preliminary results)

A plane symmetric FE model of the spot welded joint has been established (as shown in Figure 4.7) to be used in modelling the tensile shear deformation and impact deformation of the joints in the next stage. . The material properties used in this model will be predicted by the inverse FE modelling. An element type of C3D8R (a reduced- integration element used in stress/displacement analysis) was used. Due to symmetry the y-direction displacement at the mid-section (bottom surface) was set to zero. The left side of the specimen was fixed (U_Æ,¬,Ç=0) and a displacement (U_Æ=L) was applied on the movable end. The z displacement at the mid-section was set to zero. The dimensions of the welding zones were based on the micro-hardness experimental data and optical observation. All these zones were assumed to have elasto-plastic properties. The property will be predicted based on the inverse program developed described in Section 3.

Figure. 4.1 .Typical Stress-Strain curve results experiment data for dissimilar spot welding joint (MS-SS: Mild steel-Stainless steel, SS-SS: Stainless steel-Stainless steel. In this test used Stainless steel grade 304)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0 10 20 30 40

Strain

MS-SS

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Ms-Ms Ss-Ms Ss-Ss

Time g(t) Time g(t) Time g(t)

ms m/s2 ms m/s2 ms m/s2

7.6351 -10.23 7.6351 27.7 7.6351 -0.23 7.6352 -10.26 7.6352 7.45 7.6352 -0.23

7.6353 -10.24 7.6353 4.9 7.6353 -0.23

7.6354 -10.31 7.6354 12.59 7.6354 -0.23

7.6355 -10.24 7.6355 9 7.6355 -0.23

7.6356 -10.31 7.6356 14.04 7.6356 -0.23 7.6357 -10.34 7.6357 11.13 7.6357 -0.26 7.6358 -10.31 7.6358 15.33 7.6358 -0.23 7.6359 -10.39 7.6359 14.56 7.6359 -0.23

7.636 -10.36 7.636 11.81 7.636 -0.21

7.6361 -10.49 7.6361 17.42 7.6361 -0.24 7.6362 -10.34 7.6362 13.9 7.6362 -0.23 7.6363 -10.47 7.6363 11.18 7.6363 -0.23 7.6364 -10.44 7.6364 10.33 7.6364 -0.23 7.6365 -10.36 7.6365 8.48 7.6365 -0.23 7.6366 -10.62 7.6366 13.33 7.6366 -0.24 7.6367 -9.26 7.6367 15.53 7.6367 -0.24 7.6368 -8.03 7.6368 14.24 7.6368 -0.24 7.6369 -7.19 7.6369 15.48 7.6369 -0.26

7.637 -7.64 7.637 12.17 7.637 -0.23

7.6371 -8.37 7.6371 10.91 7.6371 -0.21 7.6372 -7.21 7.6372 15.76 7.6372 -0.23 7.6373 -9.57 7.6373 14.17 7.6373 -0.23 7.6374 -8.55 7.6374 13.72 7.6374 -0.23 7.6375 -5.45 7.6375 16.34 7.6375 -0.23

Figure 4.2.(a). Raw data testing results showing the difference between the three weldments in the drop weight test for dissimilar spot welding joint (Ms-Ms : Mild steel-Mild steel, MS-SS: Mild steel-Stainless steel, SS-SS: Stainless steel-Stainless steel. In this test used Stainless steel grade 304)

Figure 4.2.(b). Specimens testing results showing the difference between the three weldments in the drop weight test for dissimilar spot welding joint (A –specimen both uses material Stainless steel, B-specimens uses dissimilar material: Mild steel-Stainless steel, and C-specimens both uses material mild steel).

A B

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Filtered Row Data

Positioning 5 time pointer to mark important event

Zero acceleration Datum

From time prior to release until transducer saturation

Computed by determining the average value of data between pointers 0 and 1

Continue for entire data

Produce V(t) from data between 1 and 4

Absolute of the Min value of V(t) = max. Velocity during impact or ≥ V0 (impact Vel. At pointer 3)

Positioning Pointer 2& 3

Pointer 3 positioned where the Impact mass is thought to have made initial contact with the sample

Typically Increase in deceleration

Computing average data between pointer 2 and 3

•The Crush response defined by pointers 3 and 4 is shifted up wards by the magnitude of the measured value

•In the subsequence calculation Load, the weight of the drop mass minus any friction resistance produced by the guide rods

The crush Load as function of time P(t)

Calculated by double integration of the acceleration response between pointer 3 & 4 by the drop mass

The crush displacement as a function of time d(t)

Is calculated by double integration of the acceleration response between pointers 3& 4

Calculation as function time

The crush stress * È The strain/time history a È The Strain rate Aa AÈ⁄

* È = is calculated by dividing P(t) by the sample’s original cross section area a È = is calculated by dividing d(t) by the sample’s original height

Aa AÈ⁄ = is calculated by dividing V(t) by sample’s original height

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Figure 4.4. Comparison of the data fitting process using data acquisition and data processing on Quasi –uniform high speed foam crush testing trough a guided drop mass impact by NASA

-10 0 10 20 30 40 50

871.000 872.000 873.000 874.000 875.000 876.000

A cc e le ra ti o n , g Time, ms

2

3

4

-7.55 -7.5 -7.45 -7.4 -7.35 -7.3 -7.25

871.000 872.000 873.000 874.000 875.000 876.000

V e lo ci ty , m /s Time, ms

2

3

4

3 4

2 3 4

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(a)

(b)

(c)

Figure 4.5. Typical acceleration as function of time response highlighting the crush end. Time response Highlighting applied around, time in acceleration, which gives the value of max velocity (t= 7.6366 at MS-MS, t=7.6333 at SS-MS, t=8.6394 at SS-SS)

-11 -10 -9 -8 -7 -6 -5

7.635 7.636 7.637 7.638

A cc e le ra ti o n , m /s 2 time,ms 7.6366 -60 -40 -20 0 20 40

7.63 7.632 7.634 7.636 7.638

A cc e le ra ti o n , m /s 2 time,ms 7.6333 -0.165 -0.155 -0.145 -0.135 -0.125 -0.115 -0.105

8.636 8.646 8.656 8.666 8.676 8.686 8.696

A cc e le ra ti o n , m /s 2 Time,ms 8.6394

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(a)

(b)

(c)

Figure 4.6. Typical dynamic response crush displacement versus load as results the three weldments in the drop weight test for dissimilar spot welding joint (Ms-Ms: specimens both uses material mild steel, Ms: specimens uses dissimilar material: Mild steel-Stainless steel, and Ss-Ss: specimen both uses material Stainless steel).

1 10 100

0 0.0002 0.0004 0.0006 0.0008 0.001

Lo a d , K g f

Crush displacement, mm

Crush displacement Vs Load MS-MS

1 10 100 1000

0 0.000005 0.00001

Lo a d , K g f

Crush displacement, mm

Crush displacement Vs Load SS-MS

0.01 0.1 1 10

0 0.000005 0.00001

Lo a d , K g f

Crush displacement, mm

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Figure.4.7.Typical FE to be us welded joint.

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References :

1. ABAQUS Theory Manual 6.9

2. Alenius M., et al., 2006. Exploring the Mechanical Properties of Spot Welded Dissimilar Joints for Stainless and Galvanized Steels,Welding Journal, 305-313 3. Aravinthan A., 2003, An investigation into improve welding strength during spot

welding, Thesis, Nottingham Trent University.

4. Aslanlar S., 2006. The effect of nucleus size on mechanical properties in electrical resistance spot welding of sheets used in automotive industry, Materials and

Design,27.125-131.

5. Aslanlar S., Ogur A., U. OzsaracU., and E. Ilhan E, 2008. Welding time effect on mechanical properties of automotive sheets in electrical resistance spot welding, Materials and design, vol 29, iss 7, pg 1427-1431.

6. Bakavos D.,and Prangnell P.B., 2010. Mechanisms of joint and microstructure formation in high power ultrasonic spot welding 6111 aluminium automotive sheet. Materials Science and Engineering :A, vol.527, iss.23, pg.6320-6334. 7. Bayraktar E., Kaplan D., Grumbach M., 2004, Application of impact tensile testing

to spot welded sheets, Journal of Materials Processing Technology 153–154, 80– 86.

8. Cavalli M. N., Thouless, M. D. and Yang, Q. D., 2003, Cohesive-zone modeling of the deformation and fracture of spot-welded joints, Research Report, University of Michigan

9. Chang B.H., Zhou Y., 2003. Numerical study on the effect of electrode force in small-scale resistance spot welding, Materials processing technology , vol 139, 1-3, pg: 635-641

10.Chigurupati P., Chun B., Bandar A., 2010. Finite Element Modeling of Resistance Spot Welding Process, International Journal of Material forming, 3, 1, pp 991-994(4).

11.Chou Y., Rhee S., 2003. Relationships between quality and attributes of spot welds. Welding Journal, 195S–201S

12.Darwish S.M., 2003, Welding strengthens and balances the stresses in the spot-welded dissimilar thickness joints, J. of Materials Processing Technology 134, 352-362.

13.Dao M., et al, 2001.Computational Modelling of the forward and reverse problems in Instrumented sharp Indentation. Acta Materialia, 49, 3899-3918

14.Emmanuel H., Lamouroux J.,2007. Detailed model of spot-welded joints to simulate the failure of car assemblies, Interactive Design and manufacturing, vol.1, No.1, 33-40

15.Fan X., 2007. Simulation of distortion induced in assemblies by spot welding,

Engineering manufacture, vol 221, 8, pg 1317-1326

16.Gu Y., Nakamura T., Prchlik L., Sampath S., Wallace J., 2003, Micro-indentation and inverse analysis to characterize elastic–plastic graded materials, Materials

Science and Engineering A345, 223-233.

17.Hasanbasoglu A., 2007. Resistance spot weldability of dissimilar materials (AISI 316L–DIN EN 10130-99 steels), Materials and Design, vol 28 , Iss 6, pg 1794– 1800

18.HouZ., Kim I., Wang Y., Li C., and Chen C. , 2007. Finite element analysis for the mechanical features of resistance spot welding process, Journal of materials

(1)

(a)

(b)

(c)

1 10 100

0 0.0002 0.0004 0.0006 0.0008 0.001

Lo a d , K g f

Crush displacement, mm Crush displacement Vs Load MS-MS

1 10 100 1000

0 0.000005 0.00001

Lo a d , K g f

Crush displacement, mm Crush displacement Vs Load SS-MS

0.01 0.1 1 10

0 0.000005 0.00001

Lo a d , K g f

Crush displacement, mm Crush displacement Vs Load SS-SS

(2)

Figure.4.7.Typical FE to be us welded joint.

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1. ABAQUS Theory Manual 6.9

welding, Thesis, Nottingham Trent University.

4. Aslanlar S., 2006. The effect of nucleus size on mechanical properties in electrical resistance spot welding of sheets used in automotive industry, Materials and Design, 27.125-131.