Total Plastic Strain Research Articles

Modelling of cyclic plasticity for austenitic stainless steels 304L, 316L, 316L(N)-IG

The integrity assessment of structures subjected to cyclic loading must be verified with regard to cyclic type damage including time-independent fatigue and progressive deformation or ratcheting.Cyclic damage is verified simulating the material elastic-plastic loop and looking at the accumulated net plastic strain during each cycle at all points of the structure subjected to the complete time history of loadings.This work deals with the development of a numerical model producing the Chaboche hardening parameters starting from stress-strain data produced by testing of materials. Then, the total plastic strain can be simulated using the Chaboche inelastic constitutive model requested for finite element analyses. This is particularly demanding for pressure vessels, pressurised piping, boilers, and mechanical components of nuclear installations made of stainless steels.A design optimisation by iterative analyses is developed to approach the stress-strain test data with the Chaboche model. The parameters treated as design variables are the Chaboche parameters and the objective function to be minimised is a combination of the deviations from test data. The optimiser calls a macroinstruction simulating cyclic loading of a sample for different material temperatures.The numerical model can be used to produce hardening parameters of materials for inelastic finite element verifications of structures with complex joints like elbows subjected to a combination of steady sustained and cyclic loads.

Study on the rheological model of Xuan paper

In this paper, the creep and relaxation behaviors of Xuan paper during the stretching process were studied. The results indicated that Burgers model could describe the creep behavior of Xuan paper perfectly including elastic deformation, viscoelastic deformation and plastic deformation. For the total creep, elastic strain, viscoelastic strain and plastic strain accounted for 62–78, 17–25, and 4–13 %, respectively. At a certain temperature and humidity, elastic strain, viscoelastic strain and plastic strain increased with the increase in stress in the range of 0.2–0.8σ max, and the proportion of viscoelastic and plastic strain increased, but the proportion of elastic strain decreased. Further, the proportion of each strain tended to be stable at last. A five-element Maxwell model could describe the relaxation of Xuan paper effectively. There were few influences on the parameters of five-element Maxwell model by strain levels, so these parameters could be regarded as material constants.

Strain path effects on microstructural evolution and mechanical behaviour of constrained groove pressed aluminium sheets

Change in strain path during severe plastic deformation (SPD) of metallic materials has shown significant influence on the microstructural evolution, grain boundary characteristics and mechanical behaviour. In the present work high purity aluminium sheets are severe plastically deformed at room temperature by conventional constrained groove pressing (CGP) technique and cross-CGP technique up to 2,4, and 6 passes thereby imparting total effective plastic strain of 2.32, 4.64 and 6.96 respectively. Change in strain path is imposed during cross-CGP by rotating the sheets by ±90° along thickness axis between each pass. Microstructural evolution of processed sheets studied by electron back scattered diffraction (EBSD) analysis revealed ultra-fine grains (~1μm) irrespective of change in strain path. Analysis of grain boundary characteristics showed significant influence of strain path change on the evolution of relative fraction of low angle and high angle boundaries. The grain refinement mechanism during deformation processing in both conventional CGP and cross-CGP is corroborated to the evolution of misorientation distribution. Though considerable improvement in room temperature tensile characteristics is observed in both cases, cross-CGP processed Al sheets exhibited superior tensile properties.

Experiments and modeling of ballistic penetration using an energy failure criterion

One of the most intricate problems in terminal ballistics is the physics underlying penetration and perforation. Several penetration modes are well identified, such as petalling, plugging, spall failure and fragmentation (Sedgwick, 1968). In most cases, the final target failure will combine those modes. Some of the failure modes can be due to brittle material behavior, but penetration of ductile targets by blunt projectiles, involving plugging in particular, is caused by excessive localized plasticity, with emphasis on adiabatic shear banding (ASB).Among the theories regarding the onset of ASB, new evidence was recently brought by Rittel et al. (2006), according to whom shear bands initiate as a result of dynamic recrystallization (DRX), a local softening mechanism driven by the stored energy of cold work. As such, ASB formation results from microstructural transformations, rather than from thermal softening. In our previous work (Dolinski et al., 2010), a failure criterion based on plastic strain energy density was presented and applied to model four different classical examples of dynamic failure involving ASB formation. According to this criterion, a material point starts to fail when the total plastic strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual material mechanical behavior.The goal of this paper is to present a new combined experimental–numerical study of ballistic penetration and perforation, using the above-mentioned failure criterion. Careful experiments are carried out using a single combination of AISI 4340 FSP projectiles and 25[mm] thick RHA steel plates, while the impact velocity, and hence the imparted damage, are systematically varied. We show that our failure model, which includes only one adjustable parameter in this present work, can faithfully reproduce each of the experiments without any further adjustment.Moreover, it is shown that the most common failure criterion based on a critical strain is simply inadequate to reproduce the results, due to the linear nature of the damage evolution. The advantages of the energy-based failure criterion are discussed in detail.

Sensitivity and Correlation Analysis of Double-Layer Cylindrical Reticulated Shell considering Several Performance Functions

Reliability, sensitivity between random variables and response, and correlation between responses of double-layer cylindrical reticulated shells with three different span-to-rise ratios are deeply investigated, furthermore the effects of different kinds of random variables and different positions of random variables on reliability and sensitivity between random variable and response are also investigated in details. Cross-sectional area, yielding strength and modulus of elasticity of members and external vertical load are defined as one or more random variables respectively according to their layouts in the reticulated shells, and their effects on sensitivity are substantially carried out. Subsequently, two cases in all are taken into account based on the different classification of random variables. Three performance functions, e.g., the maximal deflection, the total plastic strain energy, the number of yielding members, are taken into consideration for two cases, and correlations among the above performance functions are investigated.

Experiments and modeling of ballistic penetration using an energy failure criterion

One of the most intricate problems in terminal ballistics is the physics underlying penetration and perforation. Several penetration modes are well identified, such as petalling, plugging, spall failure and fragmentation (Sedgwick, 1968). In most cases, the final target failure will combine those modes. Some of the failure modes can be due to brittle material behavior, but penetration of ductile targets by blunt projectiles, involving plugging in particular, is caused by excessive localized plasticity, with emphasis on adiabatic shear banding (ASB). Among the theories regarding the onset of ASB, new evidence was recently brought by Rittel et al. (2006), according to whom shear bands initiate as a result of dynamic recrystallization (DRX), a local softening mechanism driven by the stored energy of cold work. As such, ASB formation results from microstructural transformations, rather than from thermal softening. In our previous work (Dolinski et al., 2010), a failure criterion based on plastic strain energy density was presented and applied to model four different classical examples of dynamic failure involving ASB formation. According to this criterion, a material point starts to fail when the total plastic strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual material mechanical behavior. The goal of this paper is to present a new combined experimental-numerical study of ballistic penetration and perforation, using the above-mentioned failure criterion. Careful experiments are carried out using a single combination of AISI 4340 FSP projectiles and 25[mm] thick RHA steel plates, while the impact velocity, and hence the imparted damage, are systematically varied. We show that our failure model, which includes only one adjustable parameter in this present work, can faithfully reproduce each of the experiments without any further adjustment. Moreover, it is shown that the most common failure criterion based on a critical strain is simply inadequate to reproduce the results, due to the linear nature of the damage evolution. The advantages of the energy-based failure criterion are discussed in detail.

Modeling the Thermal Fields of Deposited Materials During the Spray Rolling Process

The technology of spray rolling can be applied to manufacture strips with a uniform cooling rate and a high production rate. The cooling behavior of the spray-rolled material prior to rolling contact was studied using mathematical models, tracing the accumulation of multi-layers with respect to time. Thermal history, elastic–plastic, and friction behavior of the material were considered in the complicated rolling process. The developed model had a good agreement with experimental results with potential to be utilized for prediction of the spray-rolled material thermal profile. Results show that the temperature of deposited materials prior to/or during rolling and the total equivalent plastic strain distribution in the deformation zone of deposited materials during rolling increase with increasing roller preheating temperature, the initial droplet temperature, and the mass flux distribution of the spray cone. Moreover, the deposit thickness and enthalpy remaining in the deposit are found to be the dominant influencing factors on the thermal field of deposited materials during the spray rolling process.

Characterization of localized deformation near grain boundaries of superalloy René-104 at elevated temperature

in situ surface deformation measurement techniques were applied to characterize strain localization sites in nickel-based superalloys when tested under constant load at 700°C. Deformation maps were coupled with electron backscatter diffraction (EBSD) measurement of grain location and orientation to correlate localization sites with underlying surface microstructure. Superalloy René-104 was heat treated and quenched to create two microstructures with similar grain sizes but different grain boundary character: the standard microstructure had microscopically planar grain boundaries, and the other microstructure had serrated grain boundaries. Analysis of full field strain maps calculated from in situ scanning electron microscopy (SEM) images indicated distinct differences in strain localization as a function of total strain for the two microstructures. The standard microstructure showed very little intra-granular strain accumulation, and annealing twin boundaries played an important role in strain localization sites, whereas the serrated microstructure experienced strain accumulation more evenly throughout the microstructure. Grain boundary sliding (GBS) was observed in both microstructures, but the development of serrated grain boundaries significantly decreased the contribution of this mechanism to the overall strain accommodation from 20% to 14% of the total plastic strain being accommodated by GBS.

A Material Model for Steel Plates during the Cooling Process

The time-dependent inhomogeneous temperature distribution in steel plates during the cooling increases thermal strains which, in turn, generate plastification and thus residual stresses. Moreover, phase transformation from the parent austenite phases into a product phase typically entails not only metallurgical strains but also accounts for transformation induced plasticity (TRIP), which again generates transformation related residual stresses. A unified material model that consisting of all relevant contributions to the total strain rate, i.e., elastic, plastic, thermal, metallurgical and TRIP strain contributions could be built in this paper. Transformation also released a significant amount of latent heat which naturally affected the temperature field that governed the evolution of the product phase. For the latter kinetic relationship about difference between diffusive and displacive transformation mechanisms depending on the local cooling rate is presented. Using an Avrami-like approach, the transformation kinetics is set up especially for complex cooling histories. The material model simulated the evolution of the residual stresses as well as the warping of the steel plates after completely cooling to room temperature.

Finite element modelling and experimental analysis of the processing conditions for obtaining straight blades by isothermal forging of a nanostructured aluminium-magnesium alloy

In this present study, both the design and the optimal manufacturing conditions for processing a straight blade by isothermal forging are shown. The starting material has been previously deformed by a severe plastic deformation (SPD) process known as equal channel angular extrusion (ECAE). As is well-known, the ECAE process is a technology which allows us to obtain materials with sub-micrometric grain size. These nanostructured materials can be employed afterwards as initial materials for other manufacturing processes. The use of these ultra fine grain sized materials (UFG) provides improved mechanical properties such as: greater hardness and mechanical strength, among others. In this present study, FEM simulations of the isothermal forging of an AA5083 previously deformed by ECAE will be carried out. The total equivalent plastic strain, the damage and the forces required to carry out the isothermal forging of this nanostructured aluminium alloy will be determined.

Modeling the Low Cycle Fatigue in Copper Single Crystal: Multiscale Dislocation Dynamics Simulations

ABSTRACTMultiscale dislocation dynamics plasticity (MDDP) model is used to investigate the evolution of dislocation microstructure in copper single crystals subjected to low cycle fatigue loading. Half cycle total plastic strain simulations are carried out at strain amplitudes ranging from 1×10-3 to 8×10-3. The initial hardening is investigated and the micro-structural cause behind it is presented. In addition, the loading history is presented and the effect of the initial micro-structure and dislocation distribution on the hardening behavior is studied. In addition, the evolution of the microstructures is examined. In depth analyses of the dislocation microstructures show that: 1) dislocation planes that are parallel and very close to each other are formed, 2) these walls contain dipoles that keep on zipping and unzipping during the first few cycles until they reach some stable zipping configuration. We can see that the hardening rate decreases with the increase of the number of cycles where we have large hardening rate in the first cycles then we reach to somehow constant stress. Our results are qualitatively in good agreement with recent experimental results of low cycle fatigue deformation.

炭素鋼 S45C の片振り疲労寿命に及ぼす圧縮予歪の影響

For S45C carbon steel with three heat treatments, pulsating tension tests were carried out under controlled stress condition. The effect of compressive pre-strain, Bauschinger effect and controlling factors on fatigue life were examined. The following results were obtained. The decrease of pulsating fatigue life was caused by three factors, i.e. increase of the total plastic strain amplitude, cyclic plastic strain amplitude and cyclic creep rate. The increase of Bauschinger strain led to the increase of the value of the three factors. Then it resulted in shorter fatigue life. In order to examine the cyclic stress conditions to the fatigue life, the stress ratio was defined as the ratio of maximum cyclic stress to yield stress of each material. Bauschinger strain was occurred when the stress ratio was under the threshold for each material. As the result, cyclic plastic strain amplitude and cyclic creep rate were increased and then pulsating fatigue life was reduced.

Effect of retained austenite and high temperature Laves phase on the work hardening of an experimental maraging steel

Maraging steels including the experimental alloy studied here show atypical stress–strain behaviour during tensile testing. In particular, there is a gradual decrease in the ability of the sample to support a stress following a small fraction of the total plastic strain to failure. It is demonstrated here that this phenomenon is not associated with the early onset of a necking instability, and that a large amount of the plastic strain beyond the peak stress is uniform. Investigations of microstructure and retained austenite content reveal that the intrinsic microstructure of maraging steels has a poor ability to work harden. The work hardening capacity can, as expected, be improved by introducing retained austenite, but there is an associated reduction in strength. Experiments have been designed to control the retained austenite content in such a way that clear comparisons can be made and conclusions reached on both the role of the austenite and of Laves phase generated at different temperatures.

Constraints on bed scale fracture chronology with a FEM mechanical model of folding: The case of Split Mountain (Utah, USA)

A technique is presented for improving the structural analysis of natural fractures development in large scale fold structures. A 3D restoration of a fold provides the external displacement loading conditions to solve, by the finite element method, the forward mechanical problem of an idealized rock material with a stress-strain relationship based on the activation of pervasive fracture sets. In this elasto-plasticity constitutive law, any activated fracture set contributes to the total plastic strain by either an opening or a sliding mode of rock failure. Inherited versus syn-folding fracture sets development can be studied using this mechanical model. The workflow of this methodology was applied to the Weber sandstone formation deformed by forced folding at Split Mountain Anticline, Utah for which the different fracture sets were created and developed successively during the Sevier and the syn-folding Laramide orogenic phases. The field observations at the top stratigraphic surface of the Weber sandstone lead to classify the fracture sets into a pre-fold WNW–ESE fracture set, and a NE–SW fracture set post-dating the former. The development and relative chronology of the fracture sets are discussed based on the geomechanical modeling results. Starting with a 3D restoration of the Split Mountain Anticline, three fold-fracture development models were generated, alternately assuming that the WNW–ESE fracture set is either present or absent prior to folding process. Depending on the initial fracture configuration, the calculated fracture patterns are markedly different, showing that assuming a WNW–ESE joint set to predate the fold best correlates with field observations. This study is a first step addressing the complex problem of identification of fold-related fracturing events using an elementary concept of rock mechanics. When tight to complementary field observations, including petrography, diagenesis and burial history, the approach can be used to better constrain fractured reservoir characterization.

Finite element analysis of strain distribution in ZK60 Mg alloy during cyclic extrusion and compression

Finite element method was used to study the strain distribution in ZK60 Mg alloy during multi-pass cyclic extrusion and compression (CEC). In order to optimize the CEC processing, the effects of friction condition and die geometry on the distribution of total equivalent plastic strain were investigated. The results show that the strain distributions in the workpieces are inhomogeneous after CEC deformation. The strains of the both ends of the workpieces are lower than that of the center region. The process parameters have significant effects on the strain distribution. The friction between die and workpiece is detrimental to strain homogeneity, thus the friction should be decreased. In order to improve the strain homogeneity, a large corner radius and a low extrusion angle should be used.

Neural network based modeling and optimization of deep drawing – extrusion combined process

A combined deep drawing---extrusion process is modeled with artificial neural networks (ANN's). The process is used for manufacturing synchronizer rings and it combines sheet and bulk metal forming processes. Input---output data relevant to the process was collected. The inputs represent geometrical parameters of the synchronizer ring and the outputs are the total equivalent plastic strain (TEPS), contact ratio and forming force. This data is used to train the ANN which approximates the input-output relation well and therefore can be relied on in predicting the process input parameters that will result in desired outputs provided by the designer. The complex method constrained optimization is applied to the ANN model to find the inputs or geometrical parameters that will produce the desired or optimum values of TEPS, contact ratio and forming force. This information will be very hard to obtain by just looking at the available historical input---output data. Therefore, the presented technique is very useful for selection of process design parameters to obtain desired product properties.

Application of Orthogonal Test in Numerical Simulation of Aluminum Sheet Forming

Sheet forming is a high-volume fabrication method for producing lightweight materials components. An important goal in manufacturing research is to determine the optimum method for producing products with less cost. In this paper, combined with the orthogonal test method and finite element method (FEM) simulation, the analysis was carried out to analyze the key process factors such as stamping force, fillet radius, and friction coefficient. Using orthogonal test method can reduce the testing time, learn how the molding parameters influence the total equivalent plastic strain, acquire the best match forming parameters, and give guidance for the better condition

Structural and Mechanical Behaviour of Severe Plastically Deformed OFE Copper Processed by Constrained Groove Pressing Technique

Oxygen free electrolytic (OFE) grade copper sheets (5mm thick) are severe plastically deformed by constrained groove pressing technique (CGP) at room temperature up to three passes thereby imparting a total plastic strain of 3.48 throughout the sheet material. The revelation of significant grain refinement investigated by light microscopy in constrained groove pressed sheets markedly signifies the ability of CGP technique for processing fine grained sheet materials. Relatively higher grain refinement rates are observed during initial passes. Deformation homogeneity evaluated from Vickers microhardness measurements indicated inhomogeneous deformation behaviour during early stages of straining; however enhancement in deformation homogeneity is observed later. CGP processed sheets subjected to room temperature tensile tests showed significant increase in strength associated with drop in ductility. Marginal gain in ductility coupled with slight decrease in strength attributed to the dominance of dislocation recovery is observed after third pass.

Elastic Energy Change Rate Method Research Using Energy Catastrophe Theory

The state before and after structural failure is quite different, which leads to some sudden changes to its corresponding energy. According to energy catastrophe theory, each phenomenon that reflect system state mutations can regarded as the criterion of instability. Based on the energy catastrophe theory, the problem of concrete structure failure is dealt with various energy calculation methods. Moreover, the energy change rate method is put forward to search the omen point of structure deformation and failure. By comparing with structure total strain energy and plastic strain energy, it is shown that the elastic energy change rate can determine the omen point of structure failure more easily, directly and precisely. Finally, it is found that the stress-strain relationship of many materials in engineering are quite similar, which shows that using elastic energy change rate method to determine the omen point of structure failure has some certain universality in engineering.

Plastic Deformation of 〈001〉 Single‐Crystal SrTiO3 by Compression at Room Temperature

The plastic deformation of (001) single‐crystal SrTiO3 is investigated using compression along [001] at room temperature. A total plastic strain of ∼19% ± 2% is consistently obtained. The stress–strain curve exhibiting four work‐hardening stages are describable using the stage 0 of axis rotation, the stage I “easy glide,” the stage II multiple slip and the wall‐and‐cell structure, and the stage III work softening and dynamic recovery before sample fracture takes place. It is revealed by analyzing the microstructure for each work‐hardening stage that the plastic deformation of single‐crystal SrTiO3 closely resembles that of metals. The primary slip systems of [011] and (011) predominate in stage I where plastic deformation occurs by the migration of kink pairs in collinear partial dislocations. The activation of multiple slips including [101] and (101), and [011] and (011) in stage II produces the cell‐and‐wall structure which is also characteristic of plastically deformed metals. In stage III with decreasing work‐hardening rate, the bow‐out dislocation interaction from opposite walls results in annihilation. The reaction between dislocations from adjacent walls produces the resultant dislocations with parallel to the load axis [001]. These dislocations are sessile, which eventually leads to sample fracture.