Underlying mechanism of periodical adiabatic shear bands generated in Ti–6Al–4V target by projectile impact

Highlights

• The periodical adiabatic shear bands generated in Ti–6Al–4V target was investigated.

• A newly developed stress/strain coupling accumulation failure criterion was proposed.

• The typical three stages of failure processes of the target were simulated successfully.

• Periodic change of hydrostatic pressure leads to the periodic strain accumulation.

Abstract

Periodical adiabatic shear bands are universally observed in titanium alloy targets subjected to a projectile penetration; however, the underlying mechanism is not very clear. In this letter, the response of a Ti–6Al–4V plate against a 12.7-mm armor piercing projectile is investigated, both experimentally and computationally. By introducing a newly developed stress/strain coupling accumulation failure criterion, the cratering, ductile hole enlargement, and spalling processes are simulated, showing agreement with the experimental observations. The failures of the cratering and back spalling are due to the circumferential and tensile stress accumulation damage, whereas the ductile hole enlargement occurs as a result of the periodic loading–unloading cycle of the hydrostatic pressure, thus leading to a periodic array of shear bands. Further studies show that the von Mises stress is relatively stable during the penetration, and therefore the periodic change of hydrostatic pressure leads to the periodic stress triaxiality in the target, causing the periodic strain accumulation.

Introduction

Owing to their high specific strength and excellent combination of mechanical properties, corrosion resistance, and good ballistic performance, titanium alloys are a promising alternative for lightweight armor applications [1], [2], [3]. However, because of the low thermal conductivity, they are prone to form adiabatic shear bands (ASBs) under ballistic impact. The ASB is a narrow band that develops in the vast majority of ductile materials under a high strain rate loading. It results from the competition between strain hardening, strain rate hardening, and thermo softening. As the thermo-softening effect overcomes the strain and strain rate hardening effects, an uncontrolled failure occurs [4], [5], [6].

Understanding the formation process and the distribution of the ASBs is crucial in many applications. Numerous studies have been conducted, including both experimental and theoretical analyses, and the results are well documented. Nesterenko [7], and Zheng [8], as well as Martinez [9] and Lee [10], conducted several ballistic impact tests on the Ti–6Al–4V alloy under different conditions by using a variety of bullets and fragment-simulating projectiles. The results indicated that the ASBs manifest themselves in narrow, isolated, and periodical bands with a characteristic interspacing; they are also widely observed in high-speed machining [11] and radial collapse experiments of thick-walled cylinders [12]. Further observations of the optical metallograph views of the target cross sections reported by Sukumar [13] illustrated that the angle between the ASBs and the normal direction was approximately in the range of 43°–45°. The array of ASBs exhibited a self-organized pattern with a characteristic spacing between the bands, and the comparison of the average spacing indicated that the ASBs had a more intensive spatial distribution in the targets with higher hardness. Nesterenko et al. [12] investigated the ASBs by measuring the ASB spacing in different materials, and they found that the intervals of the ASBs in Ti–6Al–4V were wider than those observed in stainless steel because of its lower hardness. Besides, the evolution pattern of the ASBs was also different for greater variations of the mechanical properties. Analyzing the distribution features of the ASBs, Singh [14] and Sun [15] reported that the formation and distribution of the ASBs were related to the distribution of the maximum shear stress in the targets during the impact. Further work conducted by Murr [16] on ballistic tests indicated that the spacing of the ASBs in the target decreased with increasing the impact velocity.

The formation and distribution of the ASBs were also theoretically analyzed and a number of theory models were proposed. The models based on the perturbation theory and on the dynamic mechanical theory were proposed by Wright–Ockendon [17] and Grady–Kipp [18], respectively. Generally, the perturbation model is suitable to address the initiation stage of the shear bands, whereas the dynamic model provides higher precision on quantifying the spacing in the subsequent development of the ASBs. Subsequently, Molinari and Batra, as well as Daridon and Zhou [19], developed a series of mathematical schemes based on the aforementioned work; numerical approaches to analyze the formation of multiple ASBs in one dimension were also proposed [19], [20].

Although progress has been made on understanding the formation and distribution of the ASBs, the underlying mechanism still requires further investigations. However, restricted by the current detecting methods, the experiments cannot directly capture the formation process of the ASBs during the impact process. On the other hand, the established theoretical models were based on some ideal assumptions, such as rate-independence linear thermal softening, or disregard of the strain hardening, and the results were inevitably limited in the description of the non-linear behavior of materials upon a high strain rate loading. Moreover, the theoretical models were unable to track the dynamic mechanical response and the damage evolution of the target. Fortunately, numerical simulations provide a powerful tool to analyze the microstructural evolution associated with the ASBs and adiabatic shear failure in ballistic tests. Although the formation process of the ASBs has been successfully modeled, most of the studies have focused on the formation of a single band under simple load conditions [21], [22] or in a predetermined position, such as the dynamic compression of a hat-shaped specimen [23], [24]. Until now, little research has been done on describing the evolution of multiple periodic ASBs under complex projectile-target interacting conditions. The manner in which the ASBs develop in the target under a ballistic impact is not very clear.

In the current study, by introducing a newly developed stress/strain coupling accumulation failure criterion, the failure process of the target and the phenomenon of the formation of periodical ASBs were successfully simulated. In contrast to the experimental and numerical results, the formation mechanism of the periodical ASBs was revealed from a mechanical point of view.