Deformation twinning during impact - numerical calculations using a constitutive theory based on multiple natural configurations

Abstract

When materials such as Armco iron, titanium etc., are subject to impact it can be observed that two basic inelastic processes take place ± slip and deformation twinning. Of these processes, inelasticity associated with the slip mechanism has received considerable attention. For example, Zerilli and Armstrong (1988) modeled the Taylor impact test for a variety of materials using traditional plasticity theories. They found that there was a signi®cant discrepancy between the theoretical and experimental results for some materials. They attributed this to the fact that they had neglected deformation twinning in their models. Subsequent metallurgical studies have indicated that twinning had indeed taken place in these materials.In this study, we focus on the inelastic processes solely due to deformation twinning (i.e., neglecting slip). We model these processes using the approach of Rajagopal and Srinivasa (1995, 1997) and Srinivasa et al., (1997), the results of which are brie¯y summarized in section 2.1. In order to better understand the twinning process, we study the Taylor impact test for a 2-D slab under the assumption that only deformation twinning takes place and solve the governing dynamical equations by using the ®nite element method. The results show that the twinned zone is concentrated near the point of impact and indeed it contributes signi®cantly to the overall permanent shape change due to the impact. Inelastic behavior of metalsIt was recognized early by researchers in metal plasticity that a difference exists between the performance of metals under static and dynamic conditions of loading. Hopkinson (1872) found that an iron wire could sustain a momentary stress of the magnitude twice as large as the elastic limit. Since then, many investigators have studied metals under static and dynamic loads. Zener and Hollomon (1944) examined the effects of strain rate and temperature on the stress-strain relation for metals undergoing slip. Based on their investigations, it is now well accepted that, for this mode of inelasticity, i.e., slip, the effect of high strain rate on the response of the material is similar to that which occurs at low temperature and at low strain rate.It has been observed (e.g., Zerilli and Armstrong 1988;Holt et al., 1994) that some materials (especially those with bcc or hcp structures) such as titanium, tantalum, depleted uranium etc., are capable of an entirely different mode of inelasticity, especially under high strain rates ± namely deformation twinning. Deformation twinning is a process by which, when the material is subjected to suf®ciently high loads, a part of a crystal may be induced to suffer a ®nite amount of simple shear across particular lattice planes in speci®c directions, these planes and directions being determined by the fact that the lattice of the product is the same as that of the parent but reoriented (see Srinivasa et al., 1997;Holt et al., 1994).Usually deformation twinning is not observed under normal temperatures and small strain rates since the material is...

Energy approach to kinetics equations for dislocations and twins and its application for high strain rate collision problems

“…Spatial distribution of twins is also nonuniform and has a tendency to macroscopic localization determined by the geometry of the problem, as well as microscopic localization on much smaller scale. Qualitatively, this distribution has a very good agreement with the calculation [29] made on the basis of an empirical model of twinning. An intensive flattening on the level of colliding base that is typical to the case of dislocation plasticity (see figure 3) combines with a wide zone of deformation.…”

Visco‐elasto‐plastic model for martensitic phase transformation in shape‐memory alloys

“…The smooth 'phase indicator' determining the dissipation potential is taken in the form (e)=0:2 tanh(150e) (34) which is nearly constant in a large neighbourhood of the wells e =±1. For simplicity, we neglect inertial forces by putting %=0 (hence Remark 1 is to be considered), which is well justiÿed except for very fast loading regimes like [42], and also we consider zero body forces by putting f =0.…”

Thermomechanics of twinning from a parent to a twin with mirror image symmetry

“…In Lapczyk et al [10] the deformation twinning is characterized like a process by which, when the material is subjected to sufficiently high loads, a part of a crystal may be induced to suffer a finite amount of simple shear across particular lattice planes in specific directions, these planes and directions being determined by the fact that the lattice of the product is the same as that of the parent but reoriented. Usually the twinning structure is not observed under the room temperature and small strain rates.…”

“…The constitutive representation postulated in (10) can be thought as a rule of mixtures for elastic materials, resulting from the elastic type constitutive equations, written with respect to the appropriate configurations, k 0 and κ α , as it follows…”

“…It is worth emphasizing some peculiar aspects related to the constitutive representation of the material response proposed in (10), or in the form (13).…”