The Kolsky compression bar, or split Hopkinson pressure bar (SHPB), is an ex- perimental apparatus used to obtain the stress-strain response of material specimens at strain rates in the order of 10 2 to 10 4 1/s. Its operation and associated data re- duction are based on principles of one-dimensional wave propagation in rods. Second order effects such as indentation of the bars by the specimen and wave dispersion in the bars, however, can significantly affect aspects of the measured material response. Finite element models of the experimental apparatus were used here to demonstrate these two effects. A procedure proposed by Safa and Gary (2010) to account for bar indentation was also evaluated and shown to improve the estimation of the strain in the bars significantly. The use of pulse shapers was also shown to alleviate the effects of wave dispersion. Combining the two can lead to more reliable results in Kolsky compression bar testing.
The work presented in this report concerns the response and failure of thin 2024- T3 aluminum alloy circular plates to a blast load produced by the detonation of a nearby spherical charge. The plates were fully clamped around the circumference and the explosive charge was located centrally with respect to the plate. The principal objective was to conduct a numerical model validation study by comparing the results of predictions to experimental measurements of plate deformation and failure for charges with masses in the vicinity of the threshold between no tearing and tearing of the plates. Stereo digital image correlation data was acquired for all tests to measure the deflection and strains in the plates. The size of the virtual strain gage in the measurements, however, was relatively large, so the strain measurements have to be interpreted accordingly as lower bounds of the actual strains in the plate and of the severity of the strain gradients. A fully coupled interaction model between the blast and the deflection of the structure was considered. The results of the validation exercise indicated that the model predicted the deflection of the plates reasonably accurately as well as the distribution of strain on the plate. The estimation of the threshold charge based on a critical value of equivalent plastic strain measured in a bulge test, however, was not accurate. This in spite of efforts to determine the failure strain of the aluminum sheet under biaxial stress conditions. Further work is needed to be able to predict plate tearing with some degree of confidence. Given the current technology, at least one test under the actual blast conditions where the plate tears is needed to calibrate the value of equivalent plastic strain when failure occurs in the numerical model. Once that has been determined, the question of the explosive mass value at the threshold could be addressed with more confidence.
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.
