True Stress-strain Behavior Research Articles

Experimental Evaluation and Prediction of Formability of Adhesive Bonded Steel Sheets at Different Adhesive Properties

Abstract The formability of adhesive bonded steel sheets is experimentally evaluated and predicted with the influence of carbon black (CB) nano powder filled adhesive. The epoxy adhesive properties are modified by filling CB nano powder at different wt. %. The tensile and in-plane plane-strain (IPPS) formability tests are carried out to evaluate the formability of adhesive bonded blanks. The true stress–strain behaviour of adhesive bonded blanks is evaluated from the experimental tests and predicted using a finite element (FE) model. The forming limit strains are evaluated during predictions by necking criteria, namely thickness gradient based necking criterion (TGNC) and effective strain-rate based necking criterion (ESRC), and validated with the experimental limit strains. The results show that the adhesive bonded blanks show improved elongation and limit strains of base materials constituting adhesive bonded blanks with increase in CB up to 2 wt. %. There is a reasonable difference in adhesive bonded sheets limit strains between predictions and experiments due to the absence of interface bonding between adhesive and base materials. In the tensile test, about 9.1 %–21.7 % variation in true major strain and about 10.3 %–13.4 % in true minor strain during TGNC predictions are noticed, while ESRC shows more variation than TGNC. In the IPPS forming test, about 8.3 %–12.4 % difference in true major strain and about 2.2 %–13.4 % difference in true minor strain are noticed during prediction by TGNC. The ESRC predictions are equally efficient as compared to TGNC predictions in this case. The TGNC shows better prediction of about 13.5 % in true major strain, and about 7.5 % in true minor strain as compared to ESRC at different adhesive properties in the tensile test. Similarly, a better prediction of about 1 % in true major strain and about 0.3 % in true minor strain in IPPS formability test is observed.

A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials.

This study offers a combined experimental and finite element (FE) simulation approach for examining the mechanical behavior of soft biomaterials (e.g. brain, liver, tendon, fat, etc.) when exposed to high strain rates. This study utilized a Split-Hopkinson Pressure Bar (SHPB) to generate strain rates of 100-1,500 sec(-1). The SHPB employed a striker bar consisting of a viscoelastic material (polycarbonate). A sample of the biomaterial was obtained shortly postmortem and prepared for SHPB testing. The specimen was interposed between the incident and transmitted bars, and the pneumatic components of the SHPB were activated to drive the striker bar toward the incident bar. The resulting impact generated a compressive stress wave (i.e. incident wave) that traveled through the incident bar. When the compressive stress wave reached the end of the incident bar, a portion continued forward through the sample and transmitted bar (i.e. transmitted wave) while another portion reversed through the incident bar as a tensile wave (i.e. reflected wave). These waves were measured using strain gages mounted on the incident and transmitted bars. The true stress-strain behavior of the sample was determined from equations based on wave propagation and dynamic force equilibrium. The experimental stress-strain response was three dimensional in nature because the specimen bulged. As such, the hydrostatic stress (first invariant) was used to generate the stress-strain response. In order to extract the uniaxial (one-dimensional) mechanical response of the tissue, an iterative coupled optimization was performed using experimental results and Finite Element Analysis (FEA), which contained an Internal State Variable (ISV) material model used for the tissue. The ISV material model used in the FE simulations of the experimental setup was iteratively calibrated (i.e. optimized) to the experimental data such that the experiment and FEA strain gage values and first invariant of stresses were in good agreement.

A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials

This study offers a combined experimental and finite element (FE) simulation approach for examining the mechanical behavior of soft biomaterials (e.g. brain, liver, tendon, fat, etc.) when exposed to high strain rates. This study utilized a Split-Hopkinson Pressure Bar (SHPB) to generate strain rates of 100-1,500 sec-1. The SHPB employed a striker bar consisting of a viscoelastic material (polycarbonate). A sample of the biomaterial was obtained shortly postmortem and prepared for SHPB testing. The specimen was interposed between the incident and transmitted bars, and the pneumatic components of the SHPB were activated to drive the striker bar toward the incident bar. The resulting impact generated a compressive stress wave (i.e. incident wave) that traveled through the incident bar. When the compressive stress wave reached the end of the incident bar, a portion continued forward through the sample and transmitted bar (i.e. transmitted wave) while another portion reversed through the incident bar as a tensile wave (i.e. reflected wave). These waves were measured using strain gages mounted on the incident and transmitted bars. The true stress-strain behavior of the sample was determined from equations based on wave propagation and dynamic force equilibrium. The experimental stress-strain response was three dimensional in nature because the specimen bulged. As such, the hydrostatic stress (first invariant) was used to generate the stress-strain response. In order to extract the uniaxial (one-dimensional) mechanical response of the tissue, an iterative coupled optimization was performed using experimental results and Finite Element Analysis (FEA), which contained an Internal State Variable (ISV) material model used for the tissue. The ISV material model used in the FE simulations of the experimental setup was iteratively calibrated (i.e. optimized) to the experimental data such that the experiment and FEA strain gage values and first invariant of stresses were in good agreement.

Details of Molecular Organization during Strain-Induced Crystallization in Natural Rubber/Clay Systems As Revealed by Real-Time Mechano-Optical Behavior

A real-time spectral birefringence technique was implemented to follow the coupled relationships among birefringence, true stress, and true strain behavior of natural rubber vulcanizates containing a series of clay concentrations. The dynamics of structural evolution was also followed by off-line wide-angle X-ray diffraction to characterize the order and orientation at different extension levels. The results show that at the same true strain level the natural rubber/organomodified clay (NR/OC) nanocomposite with higher OC content exhibits higher true stress and birefringence. While the stress optical relationship shows three different linear stages during stretching, the strain optical relationship is nonlinear and found to always exhibit a positively increasing slope with increasing strain. XRD results show higher OC-content-induced earlier appearance of strain crystallization and higher orientation factor in crystalline domains of rubber, as also evidenced by the real time birefringence results.

A procedure to determine the tangential true stress-strain behavior of pipes

Determining the tangential mechanical properties of a tube is essential for simulation of various manufacturing processes that involve the use of a tubular geometry. The aim of this study is to develop a procedure to determine the tangential true stress-strain behavior of pipes. For this purpose a modified ring test setup is proposed consisting of a ring specimen loaded with two separate D-blocks. Using a finite element model, an optimized ring specimen geometry is obtained. The optimized ring specimen exhibits uniform tangential distribution in the gauge region of the specimen and necking occurs consistently at the center of the gauge length. It is found that friction has a substantial effect on the mechanical response of the ring test for which two different setups to reduce friction are proposed. One using lubricated D-blocks (DB) and one using lubricated D-blocks with needle roller bearing (RB). Assisted by the FE model, the friction during the experiment is account for and a data analysis procedure to determine the tangential stress-strain curve of the pipe is proposed. It is found that the results using this procedure show very good agreement with previously published results.

Tensile Behavior of Polyetheretherketone over a Wide Range of Strain Rates

Polyetheretherketone (PEEK) is used in several engineering applications where it has to bear impact loads. Nevertheless, the tensile behavior has only been studied in the quasi-static range of loading rates. To address the lack of data in the impact strain rate range, the tensile mechanical behavior of PEEK is investigated at room temperature over a large range of strain rates (from 0.001 to 1000/s). The macroscopic volume change is studied under uniaxial tension using digital image correlation (DIC) method, showing a significant dilatation that reaches 16% at a logarithmic axial strain of 40%. The true stress-strain behavior is therefore established based on the measured volume change. Elsewhere, the yield stress shows a significant sensitivity to strain rate. Besides, a new constitutive equation is proposed to take into account the increase in strain rate sensitivity at high strain rates. It assumes an apparent activation volume which decreases as the strain rate increases. The new constitutive equation gives similar results when compared to the Ree-Eyring equation. However, only three material constants are to be identified and are physically interpreted.

Development of a Method to Determine the Transverse Stress-Strain Behaviour of Pipes

The aim of this study is to develop a procedure to determine the tangential true stress-strain behavior of pipes. A modified ring test setup is proposed consisting of a ring specimen loaded with two separate D-blocks. By means of a finite element model, a optimized ring specimen geometry is obtained. The optimized ring specimen exhibits uniform tangential distribution in the gauge region of the specimen and necking occurs consistently at the center of the gauge length. It is found that friction has a substantial effect on the mechanical response of the ring test. Assisted by the FE model, the friction during the experiment is account for and a data analysis procedure to determine the tangential stress-strain curve of the pipe is proposed. It is found that the results using this procedure show very good agreement with previously published results.

Determination of the intrinsic behavior of polymers using digital image correlation combined with video-monitored testing

Three methods for the determination of the large-strain behavior of ductile polymers are compared in both tension and compression. Each method relies on some (non-contact) measurement of the strain and some approximations in the calculation of stress. The strain measurement techniques include digital image correlation (DIC) and two techniques of video-based extensometry: marker tracking and area variation monitoring. Since the specimens are inevitably subject to structural plastic instabilities (necking in tension, barreling in compression) the strain and stress states are no longer uniform in the gauge section after the peak load. Under such circumstances, it is demonstrated that the three experimental methods can lead to significant differences. It is inferred from the comparative analysis that the method based on vertical marker tracking is not reliable. Validated by DIC, video-based area variation is shown to be a simple alternative way to obtain an excellent estimate of the intrinsic true stress–strain behavior of the polymer.

Cellular automata finite element (CAFE) model to predict the forming of friction stir welded blanks

The main aim of the present work is to develop a cellular automata coupled finite element (CAFE) model to predict the grain size distribution during friction stir welding (FSW) and the influence of weld defects (like voids) on the forming of FSW sheets. In order to achieve this, FSW process is simulated just by applying thermal and strain-rate analytical models on the elements constituting the FSW blanks by using ABAQUS6.8 finite element (FE) code with the help of DFLUX sub-routine. A uniform grid mesh within each finite element for cellular automata to accommodate grain size is generated for the calculation. The sheet used is Al6061-T6 with a dimension of 300×100×2.1mm. The final grain size and yield strength are predicted by generating transition rules, relating them to temperature, strain-rate and strain evolved during friction stir welding. The computed results are compared with experimental results for validation. The forming (true stress–strain) behavior was predicted for FSW blanks containing defects by two different methods and their accuracy was compared. The thermal and strain-rate models followed in this work predict the temperature and strain-rate distribution across the weld region consistently. The results are matching well with the available data. The grain size and yield strength distribution predictions through CAFE model are agreeing well with the experimental results for all the FSW conditions. The true stress–strain behavior of a FSW blank obtained from CA model (containing grain size and strength history after FSW) coincides well with the stress–strain behavior predicted from FE simulations. The CAFE model, with a stress concentration factor, successfully predicts the influence of defects on the tensile behavior. The forming behavior obtained from both the methods (METHOD 1 and METHOD 2) is coinciding well with each other, except at the initial stages of forming.

Application of Digital Marker Extensometry to Determine the True Stress-Strain Behavior of Irradiated Metals and Alloys

Abstract To study the mechanisms of deformation hardening and flow localization of radioactive materials, a noncontact “digital marker extensometry” technique has been employed. It allows researchers to easily define plasticity parameters and true stresses in experiments where highly radioactive miniature specimens are used. The engineering and “true stress-true local strain” relationships of irradiated metal polycrystals during plastic flow and hardening have been investigated experimentally after irradiation in two reactors in Kazakhstan. The true curves were obtained for copper, nickel, iron, molybdenum, as well as for the Russian stainless steels 08Cr16Ni11Mo3 and 12Cr18Ni10Ti. Describing these curves using the equation σi =σ0 + kεi demonstrates that the concept of ultimate stress in highly irradiated materials is an artifact arising from flow localization and is not fully informative of the operating hardening mechanisms.

Experimental observations of evolving yield loci in biaxially strained AA5754-O

Experimental measurement of the plastic biaxial mechanical response for an aluminum alloy (AA5754-O) sheet metal is presented. Traditional methods of multiaxial sheet metal testing require the use of finite element analysis (FEA) or other assumptions of material response to determine the multiaxial true stress versus true strain behavior of the as-received sheet material. The method used here strives to produce less ambiguous measurements of data for a larger strain range than previously possible, through a combination of the Marciniak flat bottom ram test and an X-ray diffraction technique for stress measurement. The study is performed in conjunction with a study of the microstructural changes that occur during deformation, and these microstructural results are briefly mentioned in this work. Issues of calibration and applicability are discussed, and results are presented for uniaxial (U), plane strain (PS), and balanced biaxial (BB) extension. The results show repeatable behavior (within quantified uncertainties) for U to 20%, PS to almost 15%, and BB to above 20% in-plane strains. The results are first compared with three common yield locus models (von Mises’, Hill’48, and Hosford’79), and show some unexpected results in the shape change of the yield locus at high strain levels (>5% strain). These changes include the rotation of the locus toward the von Mises surface and elongation in the balanced biaxial direction. Comparison with a more complex yield locus model (Yld2000-2d with eight adjustable parameters) showed that the locus elongation in the biaxial direction could be fit well (for a specific level of work), but at the detriment of fit to the plane strain data. Artificially large plastic strain ratios would be needed to match both the biaxial and plane strain behavior even with this more complex model.

Compressive deformation behavior of a 30 vol.%ZrC p/W composite at temperatures of 1300–1600 °C

The compressive deformation behavior of a 30 vol.%ZrC p/W composite was investigated in a temperature range of 1300–1600 °C. The true stress–strain behavior of the composite is strongly influenced by the deformation temperature and the strain rate. The serrated character of the true stress–strain curves is mainly due to the initiation, propagation and closure of microcracks in ZrC particle agglomerates during compressive deformation. The deformation mechanisms at the tested temperature range of 1300–1600 °C are the dislocation movement in the tungsten grains, slip along the W and ZrC grain boundaries as well as along ZrC/W interfaces. The dynamic recovery in the tungsten matrix is detected at the temperatures of 1300–1500 °C. The dynamic recrystallization occurs when the temperatures is above 1500 °C. The dislocation behavior in ZrC particles is also studied.

Proposed damage evolution model for large-scale finite element modeling of the dual coolant US-ITER TBM

Large-scale finite element modeling (FEM) of the US Dual Coolant Lead Lithium ITER Test Blanket Module including damage evolution is under development. A comprehensive rate-theory based radiation damage creep deformation code was integrated with the ABACUS FEM code. The advantage of this approach is that time-dependent in-reactor deformations and radiation damage can now be directly coupled with ‘material properties’ of FEM analyses. The coupled FEM–Creep damage model successfully simulated the simultaneous microstructure and stress evolution in small tensile test-bar structures. Applying the integrated Creep/FEM code to large structures is still computationally prohibitive. Instead, for thermo-structural analysis of the DCLL TBM structure the integrated FEM–creep damage model was used to develop true stress–strain behavior of F82H ferritic steel. Based on this integrated damage evolution-FEM approach it is proposed to use large-scale FEM analysis to identify and isolate critical stress areas for follow up analysis using detailed and fully integrated creep–FEM approach.

Tensile behavior of functionally graded steels produced by electroslag remelting

Tensile behavior of functionally graded steels produced by electroslag refining has been studied. Functionally graded steels containing layers of ferrite, austenite, bainite, and martensite may be fabricatedvia diffusion of alloying elements during electroslag remelting. Tensile strength of the composites depends on the composition and number of layers and those have been modeled based on the tensile behavior of individual phases. The yield stress of each element in the composites is related to the microhardness value of that element. Considering the Holloman relation for the true stress-strain behavior of each element, the tensile strength of an individual element is also related to the microhardness value of that element. By applying the rule of mixtures, the tensile strengths of the composites were determinedvia the numerical method. The obtained results are in good agreement with the experimental results.

Prediction of bending limits in friction-stir-processed thick plate aluminum

Friction-stir processing (FSP) was used to modify surface microstructures, to enhance the bending of thick-plate 6061-T6 and 7050-T7451 aluminum alloys. Plates were bent at room temperature into a V-shaped die, to various angles. Bending performance in the friction-stir-processed plates was significantly better than that in the base plates, where processing caused localized softening of the pretensile surface of the plate. A finite-element model of the plate-bending process was developed, to predict the bending limits of both the unprocessed base plates and of the friction-stir-processed plates. For the friction-stir-processed plates, the model employed a mesh divided into two or more zones; one zone was for unprocessed base material and other zones were for the processed material or for material that was affected by the heat of processing. The model used both the von Mises and the Latham and Cockroft criteria to predict bending limits. The bending-limit predictions were reasonably accurate, provided the gradient in true stress-strain behavior through the plate thickness was well characterized.

Flow behaviour of a modified Zr–2.5wt%Nb pressure tube alloy

Anisotropy in flow behavior of cold worked and stress-relieved Zr–2.5wt%Nb pressure tube alloy was characterized by performing tensile tests in the temperature range of 298–823K and under a constant nominal strain-rate of ∼3×10−4s−1. Results showed that both yield and ultimate tensile strengths of this alloy decreased gradually with increasing test temperatures, with a rapid fall in strengths above a temperature of 623K. The tensile ductility did not change appreciably up to 673K but increased rapidly above this temperature. A strain energy model was developed to explain the occurrence of dynamic strain ageing (DSA). Analysis of the true stress–strain behavior suggested that the flow hardening or softening behavior of this alloy can be expressed in the form of a constitutive relationship comprising of a constant, work-hardening term and a term representing flow softening due to recovery.

An experimental investigation of the large-strain tensile behavior of neat and rubber-toughened polycarbonate

The large-strain tensile behavior of polycarbonate and polycarbonate filled with several volume fractions ( f) of rubber particles is studied via an optical technique. Digital image correlation is used to determine, in two dimensions, the local displacement gradients and full-field displacements during a uniaxial tension test. Full-field strain contours, macroscopic true stress–strain behavior, and local volumetric strain are reduced from the raw test data. Full-field strain contours exhibit a decreasing degree of localization with increasing f. The true stress–strain results show a decrease in modulus, yield stress, post-yield strain softening, and subsequent strain hardening with increasing f. The volumetric strain decreases with increasing f as well. In the case of the neat polymer, comparisons are made to a three-dimensional finite element simulation.

The effect of natural rubber crosslink density on real time birefringence, true stress and true strain behavior

A newly developed real time spectral birefringence technique was implemented to follow the coupled relationships between birefringence, true stress and true strain behavior of varying crosslink density natural rubber vulcanizates at room temperature. It was shown that the stress optical law is valid even at early stages of crystallization during stretching and there exists a critical birefringence beyond which the metastable near perfect oriented and highly distorted crystalline regions form and upon retraction this crystalline order disappears at the same critical birefringence level. These crystalline regions exhibit nematic order with significant axial registry distortions at early stages of the formation. They are suggested to form at or near the juncture points of the chemical network formed by crosslinks, and physical network by chain entanglements where the orientability of the chains is the most efficient.

Thermomechanical behavior of virgin and highly crosslinked ultra-high molecular weight polyethylene used in total joint replacements

Three series of uniaxial tension and compression tests were conducted on two conventional and two highly crosslinked ultra-high molecular weight polyethylenes (UHMWPEs) all prepared from the same lot of medical grade GUR 1050. The conventional materials were unirradiated (control) and gamma irradiated in nitrogen with a dose of 30 kGy. The highly crosslinked UHMWPEs were gamma irradiated at room temperature with 100 kGy and then thermally processed by either annealing below the melt transition at 110°C or by remelting above the melt transition at 150°C. The true stress–strain behavior of the four UHMWPE materials was characterized as a function of strain rate (between 0.02 and 0.10 s −1) and test temperature (20–60°C). Although annealing and remelting of UHMWPE are primarily considered as methods of improving oxidation resistance, thermal processing was found to significantly impact the crystallinity, and hence the mechanical behavior, of the highly crosslinked UHMWPE. The crystallinity and radiation dose were key predictors of the uniaxial yielding, plastic flow, and failure properties of conventional and highly crosslinked UHMWPEs. The thermomechanical behavior of UHMWPE was accurately predicted using an Arrhenius model, and the associated activation energies for thermal softening were related to the crystallinity of the polymers. The conventional and highly crosslinked UHMWPEs exhibited low strain rate dependence in power law relationships, comparable to metals. In light of the unifying trends observed in the true stress–strain curves of the four materials investigated in this study, both crosslinking (governed by the gamma radiation dose) and crystallinity (governed by the thermal processing) were found to be useful predictors of the mechanical behavior of UHMWPE for a wide range of test temperatures and rates. The data collected in this study will be used to develop constitutive models based on the physics of polymer systems for predicting the thermomechanical behavior of conventional and crosslinked UHMWPE used in total joint replacements.

A notched cross weld tensile testing method for determining true stress–strain curves for weldments

Cross weld tensile testing is widely used in the industry to qualify welds. In these conventional testing fracture load is measured and the location of fracture (weld metal, base metal or heat affected zone) is evaluated. Because the load-elongation curve depends on the location of fracture and the initial gauge length, it cannot be utilized in the failure assessment of weldments. Failure assessment of weldments requires input of true stress–strain behaviour for each material zone. In this paper, a notched cross weld tensile testing method is proposed for determining the true stress–strain curve for each material zone of a weldment. In the proposed method, cylindrical cross weld tensile specimens, with a notch located either in the weld metal, base metal or possibly heat affected zone are applied. Due to the notch, plastic deformation is forced to develop in the notched region. A load versus diameter reduction curve is recorded. It has been shown that the true strain at maximum load is independent of the notch geometry. Furthermore, the materials true stress–strain curve can be determined from the recorded load versus diameter reduction curve of a notched cross weld tensile specimen by dividing a geometry-factor G, which is approximated by a quadratic function of the specimen diameter to notch radius ratio and a linear function of the true strain at the maximum load. It is found that G is independent of the material zone length when the homogenous material length is larger or equal to the minimum diameter.