Total Plastic Strain Research Articles

In-beam mechanical testing of CuCrZr

In the ITER design, CuCrZr has been selected as the heat sink material for components of the first wall and the divertor. The objective of this work is to check the material fatigue performance when the CuCrZr alloy is cyclically deformed concurrently with irradiation, using an in situ testing machine placed in a 590 MeV proton accelerator. Three fatigue experiments have been conducted at 100 °C, under strain control, at a total strain range of 0.8%. The in-beam specimen reached the longest life. The post-irradiation tested specimen had the shortest life. The total plastic strain measured in the in-beam specimen was larger than the plastic strain measured in the statically irradiated specimen or in the unirradiated specimen.

Modeling damage and deformation in impact simulations

Abstract— Numerical modeling is a powerful tool for investigating the formation of large impact craters but is one that must be validated with observational evidence. Quantitative analysis of damage and deformation in the target surrounding an impact event provides a promising means of validation for numerical models of terrestrial impact craters, particularly in cases where the final pristine crater morphology is ambiguous or unknown. In this paper, we discuss the aspects of the behavior of brittle materials important for the accurate simulation of damage and deformation surrounding an impact event and the care required to interpret the results. We demonstrate this with an example simulation of an impact into a terrestrial, granite target that produces a 10 km‐diameter transient crater. The results of the simulation are shown in terms of damage (a scalar quantity that reflects the totality of fragmentation) and plastic strain, both total plastic strain (the accumulated amount of permanent shear deformation, regardless of the sense of shear) and net plastic strain (the amount of permanent shear deformation where the sense of shear is accounted for). Damage and plastic strain are both greatest close to the impact site and decline with radial distance. However, the reversal in flow patterns from the downward and outward excavation flow to the inward and upward collapse flow implies that net plastic strains may be significantly lower than total plastic strains. Plastic strain in brittle rocks is very heterogeneous; however, continuum modeling requires that the deformation of the target during an impact event be described in terms of an average strain that applies over a large volume of rock (large compared to the spacing between individual zones of sliding). This paper demonstrates that model predictions of smooth average strain are entirely consistent with an actual strain concentrated along very narrow zones. Furthermore, we suggest that model predictions of total accumulated strain should correlate with observable variations in bulk density and seismic velocity.

Springback in v-bending: a finite element approach

Bending is one of the processes frequently applied during manufacturing of components. The bending operation involves springback, which is caused by the elastic recovery of bending deformation in metal sheets upon unloading. In the manufacturing industry, it is still a practical problem to predict the final geometry of the part after springback and to design the appropriate tooling in order to compensate for springback. In this article, a commercially available finite-element software is used to analyse bending and springback of different stainless steel grades. The amount of springback, the total equivalent plastic strains and the equivalent von Misses stresses are presented. The comparison of the FEA results with experimental finding has indicated the reliability of the finite element model proposed.

Controls on strain localization in a two‐dimensional elastoplastic layer: Insights into size‐frequency scaling of extensional fault populations

We use a two‐dimensional (2‐D) finite element code to investigate how mechanical properties and boundary conditions influence progressive strain localization during extension of a 2‐D elastoplastic layer. The deforming medium is modeled using a strain softening Von Mises rheology, with a Gaussian heterogeneity in yield strength distributed randomly in space. Specifically, we examine the effects of changing (1) the thickness of the deforming layer, (2) the basal boundary condition, (3) the range of strengths in the deforming layer, (4) the strength loss on failure, and (5) the total accommodated strain. Discrete zones of plastic shear strain are observed to nucleate and grow progressively during each experiment. In order to quantify and thus discriminate between the deformation patterns produced under differing conditions, we calculate the size‐frequency distributions of the shear band populations. Size is defined as the total plastic strain represented by each discrete structure. A wide range of size‐frequency distributions is observed, including both power law and exponential as well as distributions that show breaks in scaling with a transition from power law (at small sizes) to exponential (at large sizes). We show that these variations in population statistics are directly reflecting a change in strain localization in space and time caused by changing model parameters. Furthermore, by making an analogy between the model shear bands and tectonic faults, we provide insights into key features of fault size‐frequency distributions that have been measured in continental and oceanic extensional settings and also observed in analogue experiments.

Effects of strain and strain-rate on the formation of the shear band in metals

An experimental study on the formation of shear bands was carried out in several metals including pure titanium (α-Ti), 304 stainless steel and aluminium (Al-7075-T6) through the compression of cylinder specimens in a Split-Hopkinson-Bar system. The shear band initiation and the distribution within the specimen were examined under different plastic strains and strain rates. The shear band forms along the maximum shear stress plane. Combining the total plastic strain and the angle between the band and the centrally symmetrical axis with the stress-strain curve, the critical strain (e c ) and stress (σ c ) for the formation of the band can be evaluated. It was found that the multiple developing shear bands were stopped in front of the grain boundary in one grain of Al-7075-T6. The present experimental results agree with Armstrong's dislocation pile-up model for the initiation for shear banding. Based on dislocation dynamics, a new constitutive equation is proposed for description of the formation of shear bands. The formation of the band is caused mainly by the strain softening from the sharp increase of mobile dislocations while the thermal softening enhances the development of the shearing process.

Correlation between substructure and mechanical properties of α-Ti at varying deformation temperatures 4.2–373 K

The correlation between the substructure of α-Ti predeformed at temperature T 1 and its mechanical properties (stress of onset of plastic deformation, true rupture strength, relative elongation on subsequent deformation at the temperature T 2 varying from 4.2 to 373 K have been studied. It is shown that the changes in the mechanical properties at T 1> T 2 and T 1< T 2 are fundamentally different. In contrast to the isothermal deformation at T 2, in the T 1> T 2 case the increment in the flow stress is smaller and the total plastic strain does not exceed the highest isothermal value; conversely, at T 1< T 2 the yield stress and the total ductility surpass the isothermal level. The different predeformation effects are connected with the stability of the developed substructure against subsequent deformation: it is low if T 1> T 2 and high if T 1< T 2.

Finite element analysis of springback in bending of aluminium sheets

Bending is one of the processes frequently applied during manufacture of aluminium components. The bending operation involves springback, which is defined as elastic recovery of the part during unloading. In manufacturing industry, it is still a practical problem to predict the final geometry of the part after springback and to design appropriate tooling in order to compensate for springback. In this paper, commercially available finite-element analysis (FEA) software is used to analyse bending and springback of different aluminium materials of different thickness. The amount of springback, the total equivalent plastic strains and the equivalent von Mises stresses are presented. The FEA results are compared with empirical data.

Microstructures in an Fe Based Shape Memory Alloy and Al Based Dual Phase Crystals after High Speed Deformation

Microstructures have been examined after high-speed deformation given by free weight drop and air gun shooting. Special care was exercised to control the amount of plastic strain so that the deformed specimen could be examined as a function of total plastic strain as well as strain rate. Al based dual phase alloys of Al-Al 3 Fe, Al-Al 3 Ti and Al-Al 3 Ni have been examined both at slow and high-speed strain rates using sheet specimens of various thickness, in order to find strain rate effects on the deformability of the ordered second phase particles embedded in Al. The ordered phases, not deformable at a low strain rate in the Al based alloys, are shown to be deformed by dislocation glide in the high strain rate tests. The another aspect of the study is concerned with the mechanical and structural changes in Fe-Mn-Si based shape memory alloys by high-speed deformation. The shape recovery under the opposing stress is found to increase notably after the shape deformation given by shock loading. Also, the effect of shock loading was examined using a thin foil specimen prepared for electron microscopy. In these tests, thin foil regions were locally amorphized presumably by the heavy shear deformation induced at high strain rate.

Cyclic creep and cyclic deformation of high-strength spring steels and the evaluation of the sag effect: Part I. Cyclic plastic deformation behavior

The cyclic creep and cyclic plastic deformation behavior of two commercial suspension spring steels of high hardness levels, namely, SAE 9259 and SAE 5160, were studied under different testing conditions of cyclic peak stress and cyclic stress ratio. The experimental results indicate that both the cyclic stress ratio and cyclic peak stress have strong, but complicated, effects on the cyclic creep and cyclic plastic deformation behavior of these materials. It has also been found that the addition of silicon can increase the resistance of these steels to cyclic creep and cyclic plastic deformation, although the extent of this increase is also related to other cyclic deformation conditions. A transition in the relationship between the total plastic strain range and the cyclic stress ratio (R) has been detected at approximately R=0.5. The mechanism of such a transition is explained by the operation of cross-slip during the unloading process of cycling. Moreover, a cyclic softening behavior of these spring steels in the quench-tempered condition was also detected and is attributed to the activation and reorganization of obstacle dislocations introduced into the steels during the process of martensitic transformation. More importantly, this study has indicated that parameters such as the cyclic creep strain, the cyclic creep rate in the secondary creep stage, and the total cyclic plastic strain range can better reflect, and should be used to depict and characterize, the sag behavior of spring steels as well as other materials. Finally, the effect of silicon on sag behavior, in comparison with the results from the Bauschinger-effect test, has also been discussed through the influence of Si on carbide formation and distribution.

Low cycle fatigue resistance of Al–Li alloys

Low cycle fatigue (LCF) resistance data from binary Al–Li, ternary Al–Li–Cu, and quaternary Al–Li–Cu–Mg alloys have been compiled and discussed. The LCF resistance is measured in terms of the variation of the number of reversals to failure 2Nfwith the plastic strain amplitude Δɛp /2 as well as a modified average plastic strain energy per cycle (ΔWp )modified , obtained at different applied total strain amplitudes (Δɛt /2). The data show the effects of microstructural features, namely dominant strengthening precipitates and the degree of recrystallisation as well as crystallographic texture. Lithium content, when in excess of 2·5 wt-%in aluminium decreases the low cycle fatigue resistance the most. The degree of aging, the degree of recrystallisation, and the degree of texture also influence the LCF resistance; among which the effect of the degree of aging is the most pronounced. The effects of lithium content in aluminium solid solution and strengthening precipitates obtainable by the change in the Li/Cu ratio are found to be marginal. Based on a modified total cyclic plastic strain energy till fracture, it is shown that most of the Al–Li alloys exhibit degradation in their LCF resistance in both hypotransition (higher fatigue lives) and hypertransition (lower fatigue lives) regions. Such degradation is attributed to the combined effects of mechanical fatigue, strain localisation through dislocation–precipitate interaction, environmental effects, and finally strain localisation through the high angle grain boundaries. In comparison with the currently used 2XXX and 7XXX series aluminium alloys, Al–Li alloys require substantial improvement before they can be considered for fatigue critical applications.

Thermal Cyclic Characteristics under Load in a Ti&lt;sub&gt;50.6&lt;/sub&gt;Pd&lt;sub&gt;30&lt;/sub&gt;Ni&lt;sub&gt;19.4&lt;/sub&gt; Alloy

The thermal cyclic characteristics under load were investigated in a Ti 50.6 Pd 30 Ni 19.4 alloy. It is shown that the M s temperature, transformation strain and total plastic strain increase with increasing the number of the cycles and the increments increase with an increase of applied stress. All the above changes due to thermal cycling under load occur rapidly in the early cycles and then remain constant after a sufficiently large number of cycles. Thus, the cyclic training is effective to stabilize the martensitic transformation and shape memory characteristics of the alloy.

The separation of the fracture energy in metallic materials

The total plastic strain energy which is consumed during fracture of a plain-sided CT specimen is separated into several components. These are the energies required for deforming the specimen until the point of fracture initiation, for forming the flat-fracture surfaces, for forming the shear-lip fracture surfaces, and for the lateral contraction and the blunting at the side-surfaces, Wlat. Characteristic crack growth resistance terms, Rflat and Rslant, are determined describing the energies dissipated in a unit area of flat-fracture and slant-fracture surface, respectively. Rflat is further subdivided into the term Rsurf, to form the micro-ductile fracture surface, and into the subsurface term, Rsub, which produces the global crack opening angle. Two different approaches are used to determine the fracture energy components. The first approach is a single-specimen technique for recording the total crack growth resistance (also called energy dissipation rate). Plain-sided and side-grooved specimens are tested. The second approach rests on the fact that the local plastic deformation energy can be evaluated from the shape of the fracture surfaces. A digital image analysis system is used to generate height models from stereophotograms of corresponding fracture surface regions on the two specimen halves. Two materials are investigated: a solution annealed maraging steel V 720 and a nitrogen alloyed ferritic-austenitic duplex steel A 905. For the steel V 720 the following values are measured: Ji=65 kJ/m2, Rsurf=20 kJ/m2, Rflat=280 kJ/m2, Rslant=1000 kJ/m2, Wlat=30 J. For the steel A 905 which has no shear lips, the measured values are: Ji=190 kJ/m2, Rflat=1000 kJ/m2, and Wlat=45 J. Apart from materials characterization, these values could be useful for predicting the influence of specimen geometry and size on the crack growth resistance curves.

Simulating microstructural evolution during the hot working of alloy 718

The simulation of microstructural evolution during the primary breakdown of production-sized alloy 718 ingots and billets by radial forging was accomplished in the laboratory via multiple-stroke axial compression testing of cylindrical specimens. The dwell or hold time between strokes was varied to simulate the deformation-time history for three different locations along the radial-forging work piece: lead-end, mid-length, and tail-end positions. The microstructural evolution varied with simulated work piece position. Static, rather than dynamic, recrystallization was responsible for the observed grain-size refinement, and its repetitive occurrence during consecutive dwell periods resulted in the maintenance of a fine-grain microstructure during multiple-stroke deformation sequences. For comparison, the total plastic strain was also applied in a single-stroke test. The single- and multiple-stroke techniques gave differing microstructural results, indicating that multiple-stroke testing is necessary in modeling microstructural evolution during primary breakdown.

A strain energy-based approach to the low-cycle fatigue damage mechanism in a high-strength spring steel

Low-cycle fatigue tests were conducted using smooth, cylindrical specimens under a strain-controlled, fully reversed condition for a high-strength spring steel heat treated to different strength levels. The variation of the cyclic deformation substructure was observed with a transmission electron microscope (TEM). The results indicate that the average plastic strain energy dissipated per cycle (ΔW ps ) is an important parameter upon which a consistent evaluation of the cyclic stress-strain, the strain-life, and the plastic strain energy-life relationships is made feasible. Furthermore, the total plastic strain energy dissipated prior to failure (W f ), determined on the basis of ΔW ps , is proven to be another important parameter, from the variation of which the extent of local damage accumulation can be evaluated. Confirmed by the results of TEM observations, a strain localization-induced damage mechanism is proposed and discussed.

Flow-stress equation including effects of strain-rate and temperature history

This paper addresses effects of deformation history, temperature history and heat treatment history on the flow-stress variation in terms of the mathematical theory of plasticity. On the basis of this discussion, a new flow-stress equation taking account of effects of such histories is proposed. The equation consists of the strain rate; temperature, and the reference stress which is determined by the plastic deformation energy. The reference stress, the yield stress under the reference condition, is proposed as a measure of the history, and flow-stress is shown to depend on the reference stress but not on total plastic strain. The reference stress is shown to depend only on the generalized deformation energy, which is believed to be related to the stored energy of lattice defects introduced by plastic deformation. Plastic deformation accumulates the generalized deformation energy, and the recovery annihilates the energy. This study proposes a new flow-stress equation consisting of the reference stress, strain rate and temperature. The new flow-stress equation is applied to a forming process With varying conditions, and is consistent with experimental data. Finally, this paper provides mathematical account of the new flow-stress equation. It is shown that the deformation energy is the only parameter that can connect structural change in a lattice and the mathematical theory of plasticity. While any other parameters are possible, the deformation energy is the simplest and a justifiable parameter to evaluate the history.

Compressibility of hemp bast fibres

A force-based characterization of the extrusion pulping process is necessary to be able to predict the effects of extrusion on fibres. To determine which forces are beneficial and which only cause energy consumption, the nature and the origin of the forces have to be known. This paper discusses the behaviour of hemp bast fibres under compression to better understand the underlying mechanisms involved in the application of energy to the fibres. Untreated, water soaked and NaOH-soaked hemp bast fibres were subjected to varying loads and loading rates and the resulting stress-density and relaxation curves were studied. The stress-density relationship of hemp bast fibres was described with the compressibility equation. The coefficient of the compressibility equation decreased with temperature and moisture content. Fibres became more flexible and fibre bending became more important in the mechanism of fibre compression. The higher flexibility resulted in a lower stress over the whole density range. The compressibility equation also applied to the stress-density curve during compression of soaked fibres at low densities. However, at higher density the stress increased faster, because of flow resistance caused by the dense fibre mat. The flow limitation was advanced at higher strain rates and enhanced at higher sodium hydroxide concentrations. Relaxation was described with a generalized Maxwell model. The extent of relaxation slightly decreased with increasing maximum stress, increased with strain rate and increased with moisture content. Soaked fibres showed a much higher relaxation, which, however, was mostly caused by the high maximum stress because of the flow resistance at higher densities. When regarding the solid stress instead of the total stress, relaxation appeared to be lower. Mechanical pulping processes should therefore be operated at such low strain rates, that the stress observed only depends on the density obtained and not on the flow resistance. During repeated compression both maximum stress and the extent of relaxation decreased with the number of repetitions and the total plastic strain increased until a point was reached at which no further changes were observed. However, the total plastic strain showed a higher dependence on the maximum stress during repeated compression than on the number of compressions. Repeat compression of wet fibres resulted in the formation of a compact fibre mat with a high flow resistance causing high stress peaks.

Correlation between Strain-Based Low-Cycle Fatigue and Energy-Based Linear Damage Models

Although the potential for cumulative damage of structures during long duration earthquakes is generally recognized, most design codes do not explicitly takes into account the damage potential of such events. In this paper, a strain-based low-cycle fatigue model commonly used for the prediction of fatigue life in metals is adapted for cumulative damage assessment of structures under seismic conditions. By defining the number of load cycles in terms of the total plastic strain energy dissipated by the structure, the model is presented in a form capable of predicting the plastic strain energy capacity of the structure at the ultimate limit state. The plastic strain energy is expected to decrease rapidly with increased displacement in the small displacement range and to decrease gradually in a near linear manner with increased displacement in the large displacement range. The model is shown to calibrate reasonably well with small-scale aluminum cantilever specimens tested under large-amplitude reversed cyclic loading. At the ultimate limit state, the modified Park and Ang damage model may be considered as a linear approximation to the low-cycle fatigue model in the large displacement range.

Effect of prestrain on cyclic creep behaviour of a high strength spring steel

Cyclic creep and fracture behaviour of SAE spring steel 5160 under two prestrain conditions were studied. The cyclic creep rate, cyclic plastic strain range, total plastic strain range and cyclic creep life of the material were all found to depend strongly on the prestrain condition. It was also found that, after a certain number of cycles, cyclic hardening would reach a saturation state, followed by cyclic softening which would last until the final failure. However, a higher prestrain delayed the appearance of cyclic softening. Prestraining was also found to extend considerably the third stage of cyclic creep and thus increase the elongation to fracture of the material to the extent observed in a uniaxial tension test. Fracture surface study exhibited a mixed mode failure process and also a transition from quasi-brittle fracture at the lower prestrain, consisting of both intergranular and transgranular features, to ductile fracture at the higher prestrain, which is mainly made of dimples and is similar to that found in a uniaxial tension test. However, in the ductile fracture area, some transgranular facets and fatigue striation regions could still be observed. Finally, when the prestrain reached a certain value, compressive cyclic creep was detected and this is attributed to a strong Bauschinger effect.

Strain and strain rate behaviour of a low carbon 18Cr-12Ni stainless steel under conditions of creep low cycle fatigue interaction

Results of an investigation of the application of a low frequency “rectangular” cyclic stress, during both the initial and advanced stages of primary creep, on the time dependent strain and strain rate behaviour of a low carbon 18Cr-12Ni (304L) stainless steel are presented. The strain rates immediately before, as well as immediately after, any stress decrement or increment were measured accurately. It is shown that at any given relative amplitude of applied stress Δσ/σ and superimposed applied stress period Δt c , these strain rates depend linearly on time. The relations between these strain rates and the relative amplitude of stress cycling, Δσ/σ, are also linear at any constant cyclic loading stress period Δt c . This finding makes it possible to estimate the contribution of the net strain owing to superimposed cyclic loading to the total plastic strain. Further, it is shown that the creep strain rate after the cyclic loading superposition lasting ΣΔt c = 36 ks, is only slightly affected by this superimposed loading. An interpretation of strain and strain rate behaviour under conditions of cyclic loading superposition is based on the processes of creep strain strengthening and creep recovery, though the backward straining after any stress reduction must be taken into account as well. All the above-mentioned processes depend not only on temperature and the mean applied stress, but also on the cyclic loading history.

Cyclic plastic strain energy as a damage criterion and environmental effect in Nb-bearing high strength, low alloy steel

Low cycle fatigue behaviors in Nb-bearing high strength, low alloy (HSLA) steel have been studied at plastic strain amplitudes Δϵ p/2 ranging from 1 × 10 −5 to 1 × 10 −2 in air and in ultrahigh vacuum (UHV). Microcracks are initiated along slip lines both in air and in UHV, and grain boundaries act as effective barriers to the propagation of microcracks. Coffin-Manson relations are reasonably satisfied for the microcrack initiation life N i and the fatigue life N f both in air and in UHV. The accumulated total cyclic plastic strain energy W i required for fatigue crack initiation and the accumulated total cyclic plastic strain energy W f required for fatigue failure are expressed mathematically in the form of K( Δϵ p/2) N . The computed values of W i and W f are in good agreement with the values determined experimentally. The vacuum environment enhances N i, N f, W i and W f. The environmental effect becomes greater as the plastic strain amplitude decreases.