A.K. Pilkey

Void coalescence within periodic clusters of particles

Abstract The effect of particle clustering on void damage rates in a ductile material under triaxial loading conditions is examined using three-dimensional finite element analysis. An infinite material containing a regular distribution of clustered particles is modelled using a unit cell approach. Three discrete particles are introduced into each unit cell while a secondary population of small particles within the surrounding matrix is represented using the Gurson–Tvergaard–Needleman (GTN) constitutive equations. Deformation strain states characteristic of sheet metal forming are considered; that is, deep drawing, plane strain and biaxial stretching. Uniaxial tensile stress states with varying levels of superimposed hydrostatic tension are also examined. The orientation of a particle cluster with respect to the direction of major principal loading is shown to significantly influence failure strains. Coalescence of voids within a first-order particle cluster (consisting of three particles) is a stable event while collapse of inter-cluster ligaments leads to imminent material collapse through void-sheeting.

The co-operative role of voids and shear bands in strain localization during bending

Abstract The use of kinematic hardening is known to promote shear band formation as a result of increased yield surface curvature. Hence, the implementation of kinematic hardening in a Gurson-type model facilitates the combined effect of shear bands and voids on strain localization behaviour. An alternative formulation of the kinematic hardening Gurson–Tvergaard–Needleman (GTN) constitutive softening equations is presented herein. The resulting equations are implemented as a user material subroutine (umat) in the commercial finite element code LS-DYNA and the implementation is verified against published results. A numerical study is used to establish the role of various GTN parameters in the development of macroscopic shear localization during bending.

A linked FEM-damage percolation model of aluminum alloy sheet forming

Abstract A so-called damage percolation model is linked with a finite element model of a sheet forming process to offer a comprehensive study of ductile damage evolution. In the current study, a damage percolation code is linked with LS-DYNA, an explicit dynamic FEM code used to introduce local strain gradients and compliance effects due to damage-induced softening. The linked model utilizes a Gurson-based yield surface to account for the softening effects of void damage, while the local damage development and void linkage events are modeled using the damage percolation code. The percolation code accepts detailed second phase particle fields from image analysis of a 2.0×1.6 mm optical micrograph of AA5182 aluminum alloy sheet. The model is applied to a stretch-flange stamping process which is known to be a damage-sensitive operation. The critical conditions for fracture are predicted for various initial stretch flange hole sizes.

Numerical and experimental investigation of strain-path effects on localized deformation in steel alloys

A numerical approach to simulate texture evolution in BCC sheet materials subjected to complex forming strain paths is demonstrated. Drawing-quality (DQ) steel sheet is deformed experimentally through the application of a two-stage, orthogonal strain path. Bulk texture measurements before and after the test capture the crystallographic orientations. Both the undeformed bulk texture and the strain path are used as input for a finite element (FE)/grain model, which defines a unit cell that characterizes micro-structural material behavior. The simulated texture evolution after deformation is then compared with experimental data, and found to be in good agreement.

Effects of martensite particle size and spatial distribution on work hardening behaviour of fine-grained dual-phase steel

ABSTRACT Model dual-phase steel microstructural variants having fine ferrite grain size and a range of martensite particle sizes and spatial distributions were produced by varying the starting microstructure prior to the intercritical annealing treatment. Superior tensile properties were obtained for the microstructural variant having the smallest (∼1 µm) uniform ferrite grain structure and a corresponding uniform distribution of small (∼0.5 µm) martensite particles. This microstructural variant also exhibited superior work hardening properties, as determined from a Crussard–Jaoul analysis and plots of instantaneous work hardening exponent vs. strain. The true work hardening rate had a positive dependence on at low strain ( < 2%) for all three microstructural variants, consistent with the geometrically necessary dislocation mechanism. At higher strains, Stage III work hardening is operative and the dislocation annihilation factor exhibited a positive dependence on .

Microstructural evolution of a hot-rolled microalloyed complex phase steel

ABSTRACT The current study examines a grade of hot-rolled and continuously cooled complex phase sheet steel comprised of polygonal ferrite (PF), granular bainite (GB) and lath bainite (B). The quantity of each constituent phase depends on the thermomechanical processing conditions, which vary between commercially produced sheets. In this study, the effects of cooling rate and austenite grain morphology on microstructure are determined through a series of dilatometry experiments. The resulting CCT diagrams show a progression in the order PF → GB → B with increasing cooling rate, and that a Pancaked (unrecrystallised) austenite condition promotes the formation of PF to higher cooling rates and the formation of GB to higher temperatures. Application of the CCT results to industrially produced sheet provides a useful approach for interpreting the evolution of microstructure during controlled-cooling and coiling. However, direct comparison is limited by the moderate level of austenite pancaking that can be achieved through laboratory dilatometry experiments in comparison to an industrial hot mill. Notable differences in microstructure are observed between the leading and trailing edges of industrially produced sheets due to relatively small variations in cooling schedules.