Predicting Material Strength, Damage, and Fracture The Synergy between Experiment and Modeling George T. (Rusty) Gray III, Paul J. Maudlin, Lawrence M. Hull, Q. Ken Zuo, and Shuh-Rong Chen A metal will stretch when pulled and then return to its original shape. Elasticity allows bridges and skyscrapers to survive hurricanes, earthquakes, or even moderate explosions. But beyond a certain elongation, the metal will deform perma- nently, and under very high impact, it will shatter like glass into many small pieces. The ability to predict the results of ballistic impact depends on having a validated material-response model that describes the dynamic behavior of materials when stressed beyond their elastic limit. At Los Alamos, such a state-of-the-art capability has emerged through the interplay of new theory, advanced simulation, and high-precision measurements. The new predictive models incorporate the results of strength experiments and modern theories of crystal defect interactions and strain localizations. The models are being validated by comparisons between advanced simulations and dynamic experiments that have matching initial and boundary conditions. Predictions of metal behavior—from strain hardening to fracture—show excellent agreement with the results of small-scale impact tests, tensile tests, and explosively driven fracture of metal shells. 80 Los Alamos Science Number 29 2005 Predicting Material Strength, Damage, and Fracture rom the first time one sharp stand how the relationship between the three-dimensional (3-D) computer object was used to shape applied stress, or force over area, and simulations of these complex dynamic Fanother or cause another to the resulting strain, or change in events in place of direct experimenta- fracture, the mechanical properties length, varied with temperature, strain tion. The reasons are twofold: Either of materials—strength, ductility, and rate, and stress state. That knowledge an experiment would be prohibitively susceptibility to fracture—have was quickly applied to critical wartime expensive (a full-scale bird-ingestion shaped human history. Materials needs: high-speed manufacturing of test on a commercial jet engine con- influence human life so profoundly metal parts (including high-speed wire ducted for the Federal Aviation that some have become synonymous drawing and cold-rolling of metal Agency, for example, costs millions with different eras—the Stone Age, parts) and advances in ballistics, of dollars to field), or the system is the Bronze Age, the Iron Age, and armor, and detonation physics. too difficult to evaluate accurately the Nuclear Age. It is very possible Spinoffs from those early studies led to through experiment (for example, the that the current era, marked by peo- increasingly sophisticated materials of impact of a meteorite on the space ple’s growing dependency on elec- relevance to defense, transportation, station). In turn, the growing reliance tronics, may soon be dubbed the and communications. on 3-D simulations of complex engi- Silicon Age. In the last four decades, defense- neering systems has led to a growing During the past eras, materials oriented research has pushed the fron- demand for robust predictive material- were selected almost exclusively on tier of knowledge beyond standard response models. the basis of hands-on experience— stress-strain relationships to the com- We are developing predictive one material shows favorable prop- plex mechanisms that occur under models for mechanical behavior erties over another for a given impact, namely, deformation, damage through the interplay between sys- application. But a new capability is evolution, and fracture of metals and tematic experiments and theory. In now emerging—that of predicting alloys. The basic mechanisms control- this article, we focus most heavily material behavior and designing and ling those processes began to be on the role of experiments in devel- engineering custom materials with understood, and the resulting models oping and validating mechanical predetermined characteristics. This were used to estimate material response models. First, we present trend could, in principle, lead to the response during high-speed impact, or state-of-the-art experiments to meas- age of “predictive materials technol- high strain-rate, situations both natural ure very accurately the basic stress- ogy,” but only time will tell. What and man-made. Familiar examples strain relationships of metals and we demonstrate in this article is an include automotive crash-worthiness; alloys under varying temperatures emerging capability to predict and aerospace impacts, including foreign- and strain rates. Second, we discuss engineer the behavior of metals— object damage, such as that caused the ways in which we measure and their mechanical response under when a jet engine accidentally ingests model specific damage evolution extreme loading conditions. a bird or a meteorite impacts a satel- mechanisms that progress from the Engineering the response of metals lite; structural accelerations such as loss of load-carrying capacity to and alloys to loading is an age-old those occurring during an earthquake; fracture. Finally, we present special- trade, extending from the famous fifth high-rate manufacturing processes ized experimental methods, measure- century steels of Damascus to the alu- such as high-rate forging and machin- ments, and models describing the minum alloys that enabled the modern ing; and conventional ordinance dynamic deformation and failure era of civilian aviation. Manufacturing behavior and armor/antiarmor interac- induced by explosive deformation. recipes were typically developed tions. Within the past two decades, as Although further experimental through trial and error, but during the computer power has grown and mate- research and engineering work years leading up to World War I, scien- rials models have become more pre- remain, the efforts described here tists and engineers conducted the first dictive, the R&D community has demonstrate significant progress in systematic studies and began to under- used, wherever possible, large-scale quantifying the dynamic mechanical Number 29 2005 Los Alamos Science 81 Predicting Material Strength, Damage, and Fracture ring usually on the negative-slope side of the stress-strain curve). In fact, when an as-received material is pulled at a constant velocity at the boundaries, it follows a stress-strain curve comparable to that in Figure 1. This stress-strain path has four dis- tinct stages: (1) uniform, or homoge- neous, deformation and accumulation of background strain, (2) material instability or bifurcation (a condition that indicates loss of load-bearing capacity), (3) transition to heteroge- neous, or localized, deformation (in a normal and/or shear mode), and (4) accumulation of damage (small cracks and voids) that ultimately coa- lesces into a fracture surface. In the description of the experiments and Figure 1. Tensile Stress-Strain Curve modeling provided in the sections The tensile test is the most common test used to measure mechanical properties. below, both homogeneous and local- Round-bar or sheet samples are gripped at their ends and pulled at constant veloc- ized deformations are investigated ity (nominally, at constant strain rate) until they fail. Load and displacement of the and modeled at macroscopic scales. sample are measured and plotted as stress σ (load/cross-sectional area) vs strain ε To be predictive, those models must (sample elongation/original length). The elastic region, represented by Hooke’s law (σ = Eε, where E is an elastic constant known as Young’s modulus), is linear and capture the fundamental relationships reversible. The point of deviation from linearity is called the elastic limit and marks connecting the independent variables the onset of permanent deformation, or plastic strain. Because the onset of devia- of stress, strain rate, strain, and tem- tion is often very gradual, the “yield strength” of a metal is defined as the stress at perature to specific bulk material 0.2% permanent (or plastic) strain. Continued plastic flow beyond the elastic limit responses such as yield stress or flow produces increasing stress levels, a process called work hardening. During this stress, strain hardening, texture evolu- stage, the sample deforms uniformly, elongating and thinning while the volume tion, evolution of global damage, sub- remains constant, until work hardening can no longer keep up with the continuing sequent heterogeneous damage, such increase in stress caused by the reduction in the sample’s cross-sectional area. At as strain localization and cracking, this point, the stress goes through a maximum, called the ultimate tensile strength, and the sample begins to deform nonuniformly, or neck, before it fractures in a duc- and finally, material failure. tile manner. Necking can reflect either “normal” or shear localization preceding frac- Moreover, for the applications of ture. In soft, annealed fcc metals, the typical total plastic (or permanent) strain interest, we need to predict those immediately before fracture is 20% to 50%. responses accurately for such extreme conditions as large deformation and high strain rates, pressures, and tem- peratures. Our materials models must response of materials and applying relationship between stress (load per therefore be based on quantifiable those insights to the development unit area of material) and the resulting physical mechanisms, characterized of predictive material