Anisotropy Effect of properties on forming
1.2.6 Damage
During tensile plastic deformation, many materials suffer damage at the microstructural level. The rate at which this damage progresses varies greatly with different materials. It may be indicated by a diminution in strain-hardening in the tensile test, but as the rate of damage accumulation depends on the stress state in the process, tensile data may not be indicative of damage in other stress states.1.2.7 Rate sensitivity
As mentioned, the rate sensitivity of most sheet is small at room temperature; for steel it is slightly positive and for aluminium, zero or slightly negative. Positive rate sensitivity usually improves forming and has an effect similar to strain-hardening. As well as being indicated by the exponent m, it is also shown by the amount of extension in the tensile test-piece after maximum load and necking and before failure, i.e. E Total − E u , increases with increasing rate sensitivity.1.2.8 Comment
It will be seen that the properties that affect material performance are not limited to those that can be measured in the tensile test or characterized by a single value. Measurement of homogeneity and defects may require information on population, orientation and spatial distribution. Many industrial forming operations run very close to a critical limit so that small changes in material behaviour give large changes in failure rates. When one sample of material will run in a press and another will not, it is frequently observed that the materials cannot be distinguished in terms of tensile test properties. This may mean that one or two tensile tests are insufficient to characterize the sheet or that the properties governing the performance are only indicated by some other test.1.3 Other mechanical tests
As mentioned, the tensile test is the most widely used mechanical test, but there are many other mechanical tests in use. For example, in the study of bulk forming processes such as forging and extrusion, compression tests are common, but these are not suitable for sheet. Some tests appropriate for sheet are briefly mentioned below: • Springback. The elastic properties of sheet are not easily measured in routine tensile tests, but they do affect springback in parts. For this reason a variety of springback tests have been devised where the sheet is bent over a former and then released. • Hardness tests. An indenter is pressed into the sheet under a controlled load and the size of the impression measured. This will give an approximate measure of the hardness of the sheet – the smaller the impression, the greater the hardness. Empirical rela- tions allow hardness readings to be converted to ‘yield strength’. For strain-hardening materials, this yield strength will be roughly the average of initial yield and ultimate tensile strength. The correlation is only approximate, but hardness tests can usefully distinguish one grade of sheet from another. 12 Mechanics of Sheet Metal FormingParts
» 4f handbook jackhumechanicsofsheetmetalformingsecond
» The engineering stress–strain curve
» The true stress–strain curve
» Worked example tensile test properties
» Rate sensitivity Tensile test
» Shape of the true stress–strain curve
» Anisotropy Effect of properties on forming
» Fracture Effect of properties on forming
» Homogeneity Effect of properties on forming
» Surface effects Effect of properties on forming
» Damage Effect of properties on forming
» Rate sensitivity Effect of properties on forming
» Comment Effect of properties on forming
» Other mechanical tests 4f handbook jackhumechanicsofsheetmetalformingsecond
» Exercises 4f handbook jackhumechanicsofsheetmetalformingsecond
» Principal strain increments Uniaxial tension
» Constant volume incompressibility condition
» Stress and strain ratios isotropic material
» True, natural or logarithmic strains
» Maximum shear stress The hydrostatic stress
» The von Mises yield condition
» Relation between the stress and strain ratios
» Introduction Work of plastic deformation
» Work hardening hypothesis 4f handbook jackhumechanicsofsheetmetalformingsecond
» Effective stress and strain functions
» Summary Exercises 4f handbook jackhumechanicsofsheetmetalformingsecond
» Equal biaxial stretching, β = 1 Modes of deformation
» Plane strain, β = 0 Modes of deformation
» Uniaxial tension, β = −12 Modes of deformation
» Power law Use of a pre-strain constant
» Worked example empirical laws
» Uniaxial compression, α = −∞, β = −2 The stress diagram
» Worked example tensions Principal tensions or tractions
» Strain distributions Summary Exercises
» Introduction 4f handbook jackhumechanicsofsheetmetalformingsecond
» Thickness of the element Stress on the element Tension or traction force at a point
» Equilibrium of the element sliding on a curved surface
» Force equilibrium at the blank-holder and punch The punch force
» Tension distribution over the section
» Strain and thickness distribution
» Accuracy of the simple model Worked example 2D stamping
» Worked example Stamping a rectangular panel
» Stretch and draw ratios in a stamping Exercises
» Uniaxial tension of a perfect strip
» Worked example maximum uniform strain
» The effect of rate sensitivity
» A condition for local necking
» Strain-hardening Factors affecting the forming limit curve
» Inhomogeneity Factors affecting the forming limit curve
» Anisotropy Factors affecting the forming limit curve
» Other considerations Factors affecting the forming limit curve
» The forming window 4f handbook jackhumechanicsofsheetmetalformingsecond
» Geometry and strain in bending Plane strain bending
» Introduction Equilibrium conditions 4f handbook jackhumechanicsofsheetmetalformingsecond
» Elastic, perfectly plastic model
» Elastic bending Bending without tension
» Rigid, perfectly plastic bending
» Elastic, perfectly plastic bending
» Bending of a strain-hardening sheet
» Worked example moments Bending without tension
» Springback in an elastic, perfectly plastic material
» Residual stresses after unloading
» Reverse bending Elastic unloading and springback
» Strain distribution Small radius bends
» Stress distribution in small radius bends
» The moment curvature characteristic
» The bending line construction
» Examples of deflected shapes
» Bending a sheet in a vee-die
» Shell geometry The shell element
» Introduction Equilibrium equations 4f handbook jackhumechanicsofsheetmetalformingsecond
» Approximate models of forming axisymmetric shells
» Hole expansion Drawing Applications of the simple theory
» Summary 4f handbook jackhumechanicsofsheetmetalformingsecond
» Effect of strain-hardening Drawing the flange
» Effect of friction on drawing stress
» The Limiting Drawing Ratio and anisotropy
» Introduction Cup height 4f handbook jackhumechanicsofsheetmetalformingsecond
» Redrawing cylindrical cups 4f handbook jackhumechanicsofsheetmetalformingsecond
» Wall ironing of deep-drawn cups
» The hydrostatic bulging test
» An approximate model of bulging a circular diaphragm
» Worked example the hydrostatic bulging test
» Worked example punch stretching
» Effect of punch shape and friction
» Worked example curving an elastic, perfectly plastic sheet
» Worked example curving a strain-hardening sheet
» Introduction Bending a rigid, perfectly plastic sheet under tension
» Thickness change during bending Friction between the points A and B
» Unbending at B Worked example drawing over a radius
» Draw-beads 4f handbook jackhumechanicsofsheetmetalformingsecond
» Free expansion of a cylinder by internal pressure
» Tube forming in a frictionless die
» Tube forming with sticking friction or very high friction
» Constant thickness deformation for a tube expanded by internal pressure
» Effect of friction on axial compression
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