Localized shear in metals under impact loading

The results of studies on localized shear strain in high-strength steel, a titanium alloy, and mild sheet steel under impact loading are given. The analysis of experimental results, microstructural changes, and numerical simulation demonstrates that adiabatic shear bands formed at high-rate deformation are influenced by strain hardening and heating in plastic flow and phase transformations in a material. The distribution of temperatures in the regions of strain localization is responsible for the development of microstructural changes. Nonuniform deformation without intense strain localization develops at lower shear rates and small strain increments per loading cycle, eliminating considerable heating of a material. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 27–42, March–April, 2000.     

Regularities of the deformation of metallic materials under various conditions of static loading

The article analyzes the results of the application of the equation for describing creep of metals in various temperature and force ranges with the aid of the same numerically specified constants. An experimental evaluation is made of the possibility of describing from the same positions the regularities of instantaneous and short-term deformation, creep, stress relaxation, and creep limit.Translated from Problemy Prochnosti, No. 8, pp. 51–58, August, 1990.     

Fracture mechanisms of aluminium alloy AA7075-T651 under various loading conditions

The fracture behaviour of the aluminium alloy AA7075-T651 is investigated for quasi-static and dynamic loading conditions and different stress states. The fracture surfaces obtained in tensile tests on smooth and notched axisymmetric specimens and compression tests on cylindrical specimens are compared to the fracture surfaces that occur when a projectile, having either a blunt or an ogival nose shape, strikes a 20 mm thick plate of the aluminium alloy. The stress state in the impact tests is much more complex and the strain rate significantly higher than in the tensile and compression tests. Optical and scanning electron microscopes are used in the investigation. The fracture surface obtained in tests with smooth axisymmetric specimens indicates that the crack growth is partly intergranular along the grain boundaries or precipitation free zones and partly transgranular by void formation around fine and coarse intermetallic particles. When the stress triaxiality is increased through the introduction of a notch in the tensile specimen, delamination along the grain boundaries in the rolling plane is observed perpendicular to the primary crack. In through-thickness compression tests, the crack propagates within an intense shear band that has orientation about 45° with respect to the load axis. The primary failure modes of the target plate during impact were adiabatic shear banding when struck by a blunt projectile and ductile hole-enlargement when struck by an ogival projectile. Delamination and fragmentation of the plates occurred for both loading cases, but was stronger for the ogival projectile. The delamination in the rolling plane was attributed to intergranular fracture caused by tensile stresses occurring during the penetration event.     

Effects of environment on crack growth behaviour of superalloys under various loading conditions

Abstract

The influence of the environment on subcritical crack growth in nickel- and nickel–iron-base superalloys has been summarized. The examples of loading studied were fatigue and creep; creep–fatigue interactions were also examined. It was found that aggressive environments can either accelerate or retard crack growth. Crack retardation was caused mainly by local reduction in the driving force arising from crack deflection, crack branching, and oxide induced closure. The diffusion of, for example, oxygen along grain boundaries can accelerate crack growth. In some cases, it was possible to describe creep–fatigue interactions in terms of fatigue with hold times, using linear summation of creep crack growth and fatigue crack growth. However, exceptions to this were also found.

MST/523     

Failure behaviors of BGA solder joints under various loading conditions of high-speed shear test

Failure behaviors of ball grid array (BGA) solder ball joints under various loading conditions of high-speed shear test were investigated with an experimental and non-linear 3-dimensional finite element modeling work. A representative Pb-free solder alloy, Sn-3.0Ag-0.5Cu, was employed in this study. Far greater shear forces were measured by high-speed shear test than by low-speed shear test. The shear force further increased with shear speed mainly due to the high strain-rate sensitivity of the solder alloy. Brittle interfacial fractures can be more easily achieved by high-speed shear test, especially in higher shear speed. This was discussed with the relationship between the strain-rate and work-hardening effect and resulting stress concentration at interfacial regions. Shear force decreased with shear height, and it could be found that excessively high shear heights unfavorably affected the test results leading to unexpectedly high standard deviation values or shear tip sliding from the solder ball surface.     

Lamb waves for non-contact fatigue state evaluation of composites under various mechanical loading conditions

Methodologies for non-destructive evaluation of mechanically induced fatigue in fibre reinforced polymers are discussed. Specimens made of non-crimp glass fabric are fatigued using three different load ratios (tension–tension, tension–compression, and compression–compression). The investigation involves two loading directions (0° and 90°) of the quasi–orthotropic composite. Based on mode conversion of air-coupled ultrasound to Lamb waves, variation in a₀-mode velocity is measured in a non-contact and single-sided access configuration. The velocity measurements are performed within and outside the servo-hydraulic test rig used for inducing fatigue damage. Formation of cracks monitored in the transparent composite results in degradation of stiffness observed by the test rig. Decrease in a₀-mode velocity caused by fatigue is shown to correlate closely with stiffness degradation for all loading ratios and directions. The correlation is studied by calculating a₀-mode velocities from single-ply properties whose stiffness degradation was determined using the observed crack densities and a finite element based model.     

Stress intensity factors in two bonded elastic layers with a single edge crack under various loading conditions

In this paper, the plane problems of a single edge crack in two bonded elastic layers and in an elastic surface layer bonded to an elastic semi-infinite plane are analyzed by the body force method. The stress fields induced by a point force and a displacement discontinuity in two bonded elastic half-planes obtained by Hetenyi's solution, in other words, Green's function in closed forms, are used as fundamental solutions to solve those problems. The boundary conditions for stress free-edges of the layers and the crack surface are satisfied by superposing the distributed fundamental solutions and adjusting their densities. The stress intensity factors are systematically calculated for the various geometrical conditions and the various stiffness ratios of the layers.     

Crack–surface displacements for cracks emanating from a circular hole under various loading conditions

The purpose of this paper is to calculate and develop equations for crack–surface displacements for two‐symmetric cracks emanating from a circular hole in an infinite plate for use in strip‐yield crack‐closure models. In particular, the displacements were determined under two loading conditions: (1) remote applied stress and (2) uniform stress applied to a segment of the crack surface (partially loaded crack). The displacements were calculated by an integral‐equation method based on accurate stress–intensity factor equations for concentrated forces applied to the crack surfaces and those for remote applied stress or for a partially loaded crack surface. A boundary‐element code was also used to calculate crack–surface displacements for some selected cases. Comparisons made with crack–surface displacement equations previously developed for the same crack configuration and loading showed significant differences near the location where the crack intersected the hole surface. However, the previous equations were fairly accurate near the crack‐tip location. Herein an improved crack–surface displacement equation was developed for the case of remote applied stress. For the partially loaded crack case, only numerical comparisons were made between the previous equations and numerical integration. A rapid algorithm, based on the integral‐equation method, was developed to calculate these displacements. Because cracks emanating from a hole are quite common in the aerospace industry, accurate displacement solutions are crucial for improving life‐prediction methods based on the strip‐yield crack‐closure models.     

Structural shape determination under uncertain loading conditions

A method for the dertermination of the shape of structures is formulated in the case when the directions, positions or magnitudes of loads vary with a known probability law. By extending the criterion of the inverse-variational-problem that was proposed in the case of determinate loading conditions, the shape of a body, for which the expected value of the potential energy becomes stationary among all shapes with the same volume, is determined. For the optimization problem, displacements are assumed to be expressed as random variables. Then, a factorization of the variable loads into several fundamental loads is proposed in order to reduce the computational effort. Structures with considerably improved performance can be easily obtained, for the uncertain loading, by the present method.     

Behaviour of materials under shock loading conditions

Shock wave research is a multidisciplinary field. In materials science, it is used to study equation-of-state, phase transitions and mechanical properties. In material processing, synthesis, powder compaction, shock sintering, shock welding etc. have been the prominent applications. We have been doing shock wave research at Trombay during the last two decades. Recently, we have built a single-stage gas gun to generate shock pressures in samples. In this paper, we describe this facility and some work done on the interpretation of shock-induced phase transitions.     

Stabilized cyclic stress-strain calculation for metals under multiaxial loading

A simple plasticity model for modeling the stabilized cyclic stress-strain responses is developed to consider the effect of non-proportional additional hardening. In the proposed model, the plastic modulus for uniaxial loading is extended to multiaxial loading by introducing the non-proportionality factor and the additional hardening coefficient. The two introduced factors take into account the effects of non-proportional additional hardening, not only on the shape of the loading path, but also on the material and its microstructure. And then, the basic Armstrong-Frederick nonlinear hardening rule is modified to model the evolution of the back stress. The consistency condition is enforced to obtain the relationship between the back stress and plastic modulus. The proposed model requires only six material constants for estimating the stabilized responses. Comparisons between the test results (30CrNiMo8HH steel, SA 333 Gr.6 steel, and 1 %CrMoV steel) and model predictions show that the proposed model predicts relatively accurate stress responses under both proportional and non-proportional loading paths.