This report presents an experimental study motivated by results obtained during the 2013 Sandia Fracture Challenge. The challenge involved A286 steel, shear-dominated compression specimens whose load-deflection response contained a load maximum fol- lowed by significant displacement under decreasing load, ending with a catastrophic fracture. Blind numerical simulations deviated from the experiments well before the maximum load and did not predict the failure displacement. A series of new tests were conducted on specimens machined from the original A286 steel stock to learn more about the deformation and failure processes in the specimen and potentially improve future numerical simulations. The study consisted of several uniaxial tension tests to explore anisotropy in the material, and a set of new tests on the compression speci- men. In some compression specimen tests, stereo digital image correlation (DIC) was used to measure the surface strain fields local to the region of interest. In others, the compression specimen was loaded to a given displacement prior to failure, unloaded, sectioned, and imaged under the microscope to determine when material damage first appeared and how it spread. The experiments brought the following observations to light. The tensile tests revealed that the plastic response of the material is anisotropic. DIC during the shear- dominated compression tests showed that all three in-plane surface strain components had maxima in the order of 50% at the maximum load. Sectioning of the specimens revealed no signs of material damage at the point where simulations deviated from the experiments. Cracks and other damage did start to form approximately when the max- imum load was reached, and they grew as the load decreased, eventually culminating in catastrophic failure of the specimens. In addition to the steel specimens, a similar study was carried out for aluminum 7075-T651 specimens. These specimens achieved much lower loads and displacements, and failure occurred very close to the maximum in the load-deflection response. No material damage was observed in these specimens, even when failure was imminent. In the future, we plan to use these experimental results to improve numerical simu- lations of the A286 steel experiments, and to improve plasticity and failure models for the Al 7075 stock. The ultimate goal of our efforts is to increase our confidence in the results of numerical simulations of elastic-plastic structural behavior and failure.
Material testing using the Kolsky bar, or split Hopkinson bar, technique has proven instrumental to conduct measurements of material behavior at strain rates in the order of 103 s-1. Test design and data reduction, however, remain empirical endeavors based on the experimentalist's experience. Issues such as wave propagation across discontinuities, the effect of the deformation of the bar surfaces in contact with the specimen, the effect of geometric features in tensile specimens (dog-bone shape), wave dispersion in the bars and other particulars are generally treated using simplified models. The work presented here was conducted in Q3 and Q4 of FY14. The objective was to demonstrate the feasibility of numerical simulations of Kolsky bar tests, which was done successfully.
The objective of this project was to evaluate the use of the Johnson-Cook strength and failure models in an adiabatic finite element model to simulate the puncture of 7075- T651 aluminum plates that were studied as part of an ASC L2 milestone by Corona et al (2012). The Johnson-Cook model parameters were determined from material test data. The results show a marked improvement, in particular in the calculated threshold velocity between no puncture and puncture, over those obtained in 2012. The threshold velocity calculated using a baseline model is just 4% higher than the mean value determined from experiment, in contrast to 60% in the 2012 predictions. Sensitivity studies showed that the threshold velocity predictions were improved by calibrating the relations between the equivalent plastic strain at failure and stress triaxiality, strain rate and temperature, as well as by the inclusion of adiabatic heating.
The objective of this work was to describe several of the ductile failure criteria com- monly used to solve practical problems. The following failure models were considered: equivalent plastic strain, equivalent plastic strain in tension, maximum shear, Mohr- Coulomb, Wellman's tearing parameter, Johnson-Cook and BCJ MEM. The document presents the main characteristics of each failure model as well as sample failure predic- tions for simple proportional loading stress histories in three dimensions and in plane stress. Plasticity calculations prior to failure were conducted with a simple, linear hardening, J2 plasticity model. The resulting failure envelopes were plotted in prin- cipal stress space and plastic strain space, where the dependence on stress triaxiality and Lode angle are clearly visible. This information may help analysts select a ductile fracture model for a practical problem and help interpret analysis results.
Predicting failure of thin-walled structures from explosive loading is a very complex task. The problem can be divided into two parts; the detonation of the explosive to produce the loading on the structure, and secondly the structural response. First, the factors that affect the explosive loading include: size, shape, stand-off, confinement, and chemistry of the explosive. The goal of the first part of the analysis is predicting the pressure on the structure based on these factors. The hydrodynamic code CTH is used to conduct these calculations. Secondly, the response of a structure from the explosive loading is predicted using a detailed finite element model within the explicit analysis code Presto. Material response, to failure, must be established in the analysis to model the failure of this class of structures; validation of this behavior is also required to allow these analyses to be predictive for their intended use. The presentation will detail the validation tests used to support this program. Validation tests using explosively loaded aluminum thin flat plates were used to study all the aspects mentioned above. Experimental measurements of the pressures generated by the explosive and the resulting plate deformations provided data for comparison against analytical predictions. These included pressure-time histories and digital image correlation of the full field plate deflections. The issues studied in the structural analysis were mesh sensitivity, strain based failure metrics, and the coupling methodologies between the blast and structural models. These models have been successfully validated using these tests, thereby increasing confidence of the results obtained in the prediction of failure thresholds of complex structures, including aircraft.
Many problems of practical importance involve ductile materials that undergo very large strains, in many cases to the point of failure. Examples include structures subjected to impact or blast loads, energy absorbing devices subjected to significant crushing, cold-forming manufacturing processes and others. One of the most fundamental pieces of data that is required in the analysis of this kind of problems is the fit of the uniaxial stress-strain curve of the material. A series of experiments where mild steel plates were punctured with a conical indenter provided a motivation to characterize the true stress-strain curve until the point of failure of this material, which displayed significant ductility. The hardening curve was obtained using a finite element model of the tensile specimens that included a geometric imperfection in the form of a small reduction in the specimen width to initiate necking. An automated procedure iteratively adjusted the true stress-strain curve fit used as input until the predicted engineering stress-strain curve matched experimental measurements. Whereas the fitting is relatively trivial prior to reaching the ultimate engineering stress, the fit of the softening part of the engineering stress-stain curve is highly dependent on the finite element parameters such as element formulation and initial geometry. Results by two hexahedral elements are compared. The first is a standard, under-integrated, uniform-strain element with hourglass control. The second is a modified selectively-reduced-integration element. In addition, the effects of element size, aspect ratio and hourglass control characteristics are investigated. The effect of adaptively refining the mesh based on the aspect ratio of the deformed elements is also considered. The results of the study indicate that for the plate puncture problem, characterizing the material with the same element formulation and size as used in the plate models is beneficial. On the other hand, using different element formulations, sizes or initial aspect ratios can lead to unreliable results.
Interfacial delamination is often the critical failure mode limiting the performance of polymer/metal interfaces. Consequently methods that measure the toughness of such interfaces are of considerable interest. One approach for measuring the toughness of a polymer/metal interface is to use the stressed-overlayer test. In this test a metal substrate is coated with a sub-micron thick polymer film to create the interface of interest. An overlayer, typically a few tenths of a micron of sputtered tungsten, is then deposited on top of the polymer in such a way as to generate a very high residual compressive stress within the sputtered layer ({approx} 1-2 GPa). This highly stressed overlayer induces delamination and blister formation. The measured buckle heights and widths are then used in conjunction with a fracture mechanics analysis to infer interfacial toughness. Here we use a finite element, cohesive-zone-based, fracture analysis to perform the required interfacial crack growth simulation. This analysis shows that calculated crack growth is sensitive to the polymer layer thickness even when the layer is only 10's of nanometers thick. The inward displacement of the overlayer at the buckle edge, which is enabled by the relatively low polymer compliance, is the primary cause of differences from a rigid substrate idealization.
Film durability is a primary factor governing the use of emerging thin film flexible substrate devices where compressive stresses can lead to delamination and buckling. It is of particular concern in gold film systems found in many submicron and nanoscale applications. We are therefore studying these effects in gold on PMMA systems using compressively stressed tungsten overlayers to force interfacial failure and simulations employing cohesive zone elements to model the fracture process. Delamination and buckling occurred spontaneously following deposition with buckle morphologies that differed significantly from existing model predictions. Moreover, use of thin adhesive interlayers had no discernable effect on performance. In this presentation we will use observations and simulations to show how substrate compliance and yielding affects the susceptibility to buckling of gold films on compliant substrates. We will also compare the fracture energies and buckle morphologies of this study with those of gold films on sapphire substrates to show how changing substrate compliance affects buckle formation.
Deformation and fracture of thin films on compliant substrates are key factors constraining the performance of emerging flexible substrate devices. These systems often contain layers of thin polymer, ceramic and metallic films and stretchable interconnects where differing properties induce high normal and shear stresses. As long as the films remain bonded to the substrates, they may deform far beyond their freestanding form. Once debonded, substrate constraint disappears leading to film failure. Experimentally it is very difficult to measure properties in these systems at sub-micron and nanoscales. Theoretically it is very difficult to determine the contributions from the films, interfaces, and substrates. As a result our understanding of deformation and fracture behavior in compliant substrate systems is limited. This motivated a study of buckle driven delamination of thin hard tungsten films on pure PMMA substrates. The films were sputter deposited to thicknesses of 100 nm, 200 nm, and 400 nm with a residual compressive stress of 1.7 GPa. An aluminum oxide interlayer was added on several samples to alter interfacial composition. Buckles formed spontaneously on the PMMA substrates following film deposition. On films without the aluminum oxide interlayer, an extensive network of small telephone cord buckles formed following deposition, interspersed with regions of larger telephone cord buckles. On films with an aluminum oxide interlayer, telephone cord buckles formed creating a uniform widely spaced pattern. Through-substrate optical observations revealed matching buckle patterns along the film-substrate interface indicating that delamination occurred for large and small buckles with and without an interlayer. The coexistence of large and small buckles on the same substrate led to two distinct behaviors as shown in Figure 2 where normalized buckle heights are plotted against normalized film stress. The behaviors deviate significantly from behavior predicted by rigid elastic solutions. To address this issue we developed a finite element analysis technique that employed a cohesive zone model to simulate interfacial crack growth. Specifying the traction-separation relationship, cohesive strength, and work of separation along with film thickness, film stress, and film and substrate properties, buckle width and height were determined as a function of interfacial toughness. The simulations indicate that an analysis based on rigid substrate solutions significantly underestimate toughness for prescribed buckle widths: a result consistent with an analysis by Yu and Hutchinson that pieced together a solution based on non-linear plate theory with a solution for the linear film on substrate problem. More importantly, the results defined a lower limiting bound to seemingly disparate buckle deflection data. The variance from linear elastic behavior, especially for the small buckles, indicates more than substrate compliance is controlling behavior. Comparison of the experimental results with cohesive zone simulations suggests that the two buckle behaviors are associated with different levels of substrate yielding. In this presentation we will use the results to show how substrate compliance and deformation affect delamination and buckling of films on compliant substrates and provide a means to predict device performance.
This report considers the calculation of the quasi-static nonlinear response of rectangular flat plates and tubes of rectangular cross-section subjected to compressive loads using quadrilateralshell finite element models. The principal objective is to assess the effect that the shell drilling stiffness parameter has on the calculated results. The calculated collapse load of elastic-plastic tubes of rectangular cross-section is of particular interest here. The drilling stiffness factor specifies the amount of artificial stiffness that is given to the shell element drilling Degree of freedom (rotation normal to the plane of the element). The element formulation has no stiffness for this degree of freedom, and this can lead to numerical difficulties. The results indicate that in the problems considered it is necessary to add a small amount of drilling tiffness to obtain converged results when using both implicit quasi-statics or explicit dynamics methods. The report concludes with a parametric study of the imperfection sensitivity of the calculated responses of the elastic-plastic tubes with rectangular cross-section.
Development of flexible thin film systems for biomedical, homeland security and environmental sensing applications has increased dramatically in recent years [1,2,3,4]. These systems typically combine traditional semiconductor technology with new flexible substrates, allowing for both the high electron mobility of semiconductors and the flexibility of polymers. The devices have the ability to be easily integrated into components and show promise for advanced design concepts, ranging from innovative microelectronics to MEMS and NEMS devices. These devices often contain layers of thin polymer, ceramic and metallic films where differing properties can lead to large residual stresses [5]. As long as the films remain substrate-bonded, they may deform far beyond their freestanding counterpart. Once debonded, substrate constraint disappears leading to film failure where compressive stresses can lead to wrinkling, delamination, and buckling [6,7,8] while tensile stresses can lead to film fracture and decohesion [9,10,11]. In all cases, performance depends on film adhesion. Experimentally it is difficult to measure adhesion. It is often studied using tape [12], pull off [13,14,15], and peel tests [16,17]. More recent techniques for measuring adhesion include scratch testing [18,19,20,21], four point bending [22,23,24], indentation [25,26,27], spontaneous blisters [28,29] and stressed overlayers [7,26,30,31,32,33]. Nevertheless, sample design and test techniques must be tailored for each system. There is a large body of elastic thin film fracture and elastic contact mechanics solutions for elastic films on rigid substrates in the published literature [5,7,34,35,36]. More recent work has extended these solutions to films on compliant substrates and show that increasing compliance markedly changes fracture energies compared with rigid elastic solution results [37,38]. However, the introduction of inelastic substrate response significantly complicates the problem [10,39,40]. As a result, our understanding of the critical relationship between adhesion, properties, and fracture for hard films on compliant substrates is limited. To address this issue, we integrated nanomechanical testing and mechanics-based modeling in a program to define the critical relationship between deformation and fracture of nanoscale films on compliant substrates. The approach involved designing model film systems and employing nano-scale experimental characterization techniques to isolate effects of compliance, viscoelasticity, and plasticity on deformation and fracture of thin hard films on substrates that spanned more than two orders of compliance magnitude exhibit different interface structures, have different adhesion strengths, and function differently under stress. The results of this work are described in six chapters. Chapter 1 provides the motivation for this work. Chapter 2 presents experimental results covering film system design, sample preparation, indentation response, and fracture including discussion on the effects of substrate compliance on fracture energies and buckle formation from existing models. Chapter 3 describes the use of analytical and finite element simulations to define the role of substrate compliance and film geometry on the indentation response of thin hard films on compliant substrates. Chapter 4 describes the development and application of cohesive zone model based finite element simulations to determine how substrate compliance affects debond growth. Chapter 5 describes the use of molecular dynamics simulations to define the effects of substrate compliance on interfacial fracture of thin hard tungsten films on silicon substrates. Chapter 6 describes the Workshops sponsored through this program to advance understanding of material and system behavior.