Introduction and structure of the research work

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 reverseinverse 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 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 = • 8Œ• ≤ 6 r _ 8Œ• 6 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 = 6 + Ÿ 3.2 For continuity at yielding, the following condition must hold = 6 6 = 6 = r 6 _ 3.3 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: = , 6 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