Total Plastic Strain Energy Research Articles

Lifetime Prediction Method of the Traction Converter IGBT Based on Plastic Strain Energy Density

Insulated gate bipolar transistor (IGBT) is the most important power electronic component in the traction converters of trains. During the operation of the IGBT, the solder layer is continuously subjected to alternating stress, which eventually leads to the fatigue failure of the solder layer. Therefore, an accurate assessment of the lifetime of the IGBT module solder layer is of great importance for the safe and reliable operation of the trains. Firstly, the micromechanism of the plastic deformation of the base solder layer of the IGBT module is introduced, as well as the lifetime model based on the plastic strain energy density. Then the total plastic strain energy density of the base solder layer is determined by conducting the accelerated aging tests on the IGBT module and combining the finite element simulation results. Meanwhile, the relationship between different aging degrees of the base solder layer of the IGBT module and the plastic strain energy density is studied by finite element simulation. Then, the lifetime of the base solder layer at different aging stages is calculated based on the above results so that the total lifetime of the IGBT module is obtained. Finally, the predicted lifetime of the IGBT module by the proposed method is compared with the lifetime obtained by the accelerated aging test and compared with the traditional lifetime prediction method based on the Coffin-Manson-Arrhenius model. The comparison results verify the accuracy of the proposed lifetime prediction method in this paper.

Low cycle fatigue performance of DP900 steel under cyclic shear paths

AbstractIn this study, a sheet fatigue shear test device is designed and applied to the low‐cycle fatigue testing of DP900 with varying strain amplitudes within the range of 0.5%–6.0%. The microstructure is analyzed by using electron backscatter diffraction, and fracture surfaces are examined via scanning electron microscopy. Results indicate that the material exhibits cyclic softening behavior after the first two cycles of hardening, with a stable softening rate and a high damage evolution rate related to loading amplitude. The variation of the hysteresis curve in the cyclic process is shown. Total plastic strain energy absorbed increases as loading amplitude decreases and it reaches the peak at approximately 1%. The life prediction model based on plastic strain energy density and strain amplitude is verified to be suitable for the cyclic shear path. The influence of microinhomogeneity on the distribution of stress and strain, especially the deformation of martensite, is closely related to the bi‐linear region of fatigue life curve.

Investigation of creep-fatigue crack growth of G115 steel using a novel damage model

The flexible operation of power-plant structures could cause creep-fatigue crack propagation, which is a major concern for design and maintenance. Therefore, this study investigated the crack propagation in G115 steel under isothermal creep-fatigue loading by using a novel damage model. Creep and fatigue damage were determined by the exhaustion of the creep ductility and the total plastic strain energy during the crack growth process, respectively. The crack propagation behavior was simulated by the finite element method, and the calculated data were compared with experimental results, which demonstrated the high precision of this model. The calculated damage values at the crack tip were analyzed, and the creep damage (cavities) around the main crack under 60 and 600 s hold times were observed based on X-ray micro-computed tomography. The cavity density for the test with 600 s of holding was obviously larger than that for the 60 s dwell test, with the former showing more significant creep damage. Calculations of compact tension specimens with different hold times, specimen thicknesses, and crack lengths were further conducted and analyzed. The results revealed that increasing the hold times, specimen thicknesses, and crack lengths increased the cyclic crack growth rate.

Distribution of Optimum Yield-Strength and Plastic Strain Energy Prediction of Hysteretic Dampers in Coupled Shear Wall Buildings

The structural behavior of reinforced concrete coupled shear wall structures is greatly influenced by the behavior of their coupling beams. This paper presents a process of the seismic analysis of reinforced concrete coupled shear wall-frame system linked by hysteretic dampers at each floor. The hysteretic dampers are located at the middle portion of the linked beams which most of the inelastic damage would be concentrated. This study concerned particularly with wall-frame structures that do not twist. The proposed method, which is based on the energy equilibrium method, offers an important design method by the result of increasing energy dissipation capacity and reducing damage to the wall’s base. The optimum distribution of yield shear force coefficients is to evenly distribute the damage at dampers over the structural height based on the cumulative plastic deformation ratio of the dissipation device. Nonlinear dynamic analysis indicates that, with a proper set of damping parameters, the wall’s dynamic responses can be well controlled. Finally, based on the total plastic strain energy and its trend through the height of the buildings, a prediction equation is suggested.

Low-cycle multiaxial fatigue behaviour and fatigue life prediction for CuZn37 brass using the stress-strain models

The low-cycle, strain-controlled fatigue tests have been conducted on CuZn37 brass (ASTM: C27200, EN: CW508L). Machined specimens have been subjected to uniaxial, proportional and non-proportional axial-torsional loadings. The monotonic and cyclic material properties have been determined for the loadings used. The obtained fatigue lives have been analysed in reference to the total Huber-von Mises equivalent strain ranges, the hysteresis loops energy in the loading cycle and the total plastic strain energy in the fatigue test. The relations between the plastic strain energy and the total as well as the plastic strain have been described. On the basis of the obtained experimental results, the selected stress-strain multiaxial fatigue criteria have been evaluated. In the conclusion it was found that fatigue lives predicted using the Fatemi-Socie and Garud criteria are closest to the experimental ones.

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.

Low cycle fatigue properties and an energy-based approach for as-extruded AZ31 magnesium alloy

Low cycle fatigue tests were conducted to investigate the cyclic deformation behavior and the energy-based criterion of AZ31 magnesium alloy. The alloy exhibited an asymmetric hysteresis loop due to the twinning and detwinning effect. The cyclic stress responses showed cyclic hardening at all total strain amplitudes. To evaluate the plastic strain energy, the Halford-Morrow equation and a modified equation for magnesium alloy were compared. The effect of twinning on the total plastic strain energy dissipated during fatigue life was discussed. The variations of the twin and dislocation densities were also investigated using optical microscopy and transmission electron microscopy, respectively.

Experimental investigation on the effect of tensile pre-strain on ratcheting behavior of 430 Stainless Steel under fully-reversed loading condition

In this paper, the effect of the tensile pre-strain on ratcheting process in 430 Stainless Steel was examined by performing a series of fully tensile–compression cyclic loading tests on the tested material with three tensile pre-strain levels or no prior deformation. The experimental results indicate that a compressive cyclic creep occurs in all applied cases for the tested material without pre-strain. Clearly, the observation reflects that the tested material exists the an-isotropic in tension and compression. Furthermore, for the tested material with various value of pre-strain, cyclic creep can also be found and the direction of creep deformation is always opposite to that of the given pre-strain. From an experimental observation on the residue deformation produced by cyclic creep, it is found that the stable total compressive creep strain scaled with increasing tensile pre-strains at the same stress amplitude condition. The material with greater compressive creep strain responded to the same applied tensile pre-strain level with higher controlled stress amplitude. Exploring the effects of the tensile pre-strain on the stable stress–strain response, this paper has been focused on those items. They are the strain range, Δ ε , plastic strain range, Δ ε p , and plastic strain energy density, Δ W P at half-life. Experimental results show that the material with different tensile pre-strains or without pre-strain had a higher response when the applied stress amplitude range was increased. Those indicated material responses have increased at increasing tensile pre-strain. In observation the effects of tensile pre-strain on the fatigue, it is found that the effect of the tensile pre-strain is to reduce the cycles to failure. A decreasing fatigue life is observed with increasing the tensile pre-strain level. In the domain of high-cycle fatigue life (in the range of 10 5–10 7 cycles), the effect of tensile pre-strain on degrading fatigue life is obvious and the degree of reducing fatigue life is governed by the magnitude of the stress amplitude. Moreover, the damage parameter based on the total plastic strain energy, W f = ∑ Δ W p , can produce satisfactory life prediction results for 430 Stainless Steel with a tensile pre-strain effect under fully reversed tension–compression loading condition.

Interior wide beam-column connections in existing RC frames subjected to lateral earthquake loading

The seismic performance of two RC interior wide beam-column connections representative of existing frames designed and detailed according to past construction practices in the moderate-seismicity Mediterranean area was investigated experimentally. The specimens were subjected to axial loads, moderate levels of gravity loading and cyclic displacements up to failure. The specimens exhibited a “strong column-weak beam” type of flexural yielding mechanism. The wide beams did not reach the expected capacities corresponding to the formation of a full-width plastic hinge. The wide-beam longitudinal bars exhibited significant slippage, and the transverse beams underwent severe torsion cracking and even failure; this caused severe pinching in the load versus displacement hysteretic loops and exacerbated the intrinsic flexibility of this type of connection. The average drift ratios at first yielding of the wide beam longitudinal reinforcement and at failure were 2.7 and 4.5%, respectively. The displacement ductility ratio was about 2.8. The ultimate energy dissipation capacity of each specimen—obtained by dividing the total plastic strain energy by the product of the yield load and yield displacement—was approximately 9, which is about one fourth of the value recommended for providing adequate seismic performance. Finally, a simple approach is suggested for prediction of the bending capacity of existing connections.

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.

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.

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.

An optical-fiber fatigue crack-detection and monitoring system: Hale, K.F. Smart Mater. Struct. June 1992, (2), 156–161

The low cycle fatigue (LCF) and high cycle fatigue (HCF) properties of Al–Li alloys are influenced by alloy composition, microstructural characteristics, tensile stretching prior to artificial aging, and crystallographic texture. In general the fatigue properties, notably the notched HCF resistances, of Al–Li alloys are similar to those of conventional aerospace aluminium alloys. Alloy development programs on newer Al–Li alloys aim to study further the effects of minor alloying additions (rare earths, beryllium, silver and TiB); various thermomechanical treatments; alloy microstructure, notably crystallographic texture and grain size; and the fatigue load history and environment on the mechanical behavior, including the fatigue properties. It is important to note that the occurrence of bilinearity in LCF life-dependence on strain amplitude in most Al–Li alloys engenders the overestimation of the LCF lives in both the hypo-transition (lower strain amplitudes; longer fatigue lives) and hyper-transition (higher strain amplitudes; shorter fatigue lives) regions if the lives are estimated by extrapolation from either of these regions. Further, in cases such as in Al-Li alloys where there are large differences in strength-based (Basquin-like) and plastic strain – based (Coffin-Manson) power-law relationships, it is appropriate to develop an alloy design philosophy based on either plastic strain energy per cycle (Halford-Morrow) or fatigue toughness (total plastic strain energy to fracture). All of these aspects are discussed in detail in this chapter.

Fatigue in single crystal nickel superalloys. Interim report, 16 March–15 April 1992: Annis, C. AD-A250 068/4/XAB (1992) 10 pp

The low cycle fatigue (LCF) and high cycle fatigue (HCF) properties of Al–Li alloys are influenced by alloy composition, microstructural characteristics, tensile stretching prior to artificial aging, and crystallographic texture. In general the fatigue properties, notably the notched HCF resistances, of Al–Li alloys are similar to those of conventional aerospace aluminium alloys. Alloy development programs on newer Al–Li alloys aim to study further the effects of minor alloying additions (rare earths, beryllium, silver and TiB); various thermomechanical treatments; alloy microstructure, notably crystallographic texture and grain size; and the fatigue load history and environment on the mechanical behavior, including the fatigue properties. It is important to note that the occurrence of bilinearity in LCF life-dependence on strain amplitude in most Al–Li alloys engenders the overestimation of the LCF lives in both the hypo-transition (lower strain amplitudes; longer fatigue lives) and hyper-transition (higher strain amplitudes; shorter fatigue lives) regions if the lives are estimated by extrapolation from either of these regions. Further, in cases such as in Al-Li alloys where there are large differences in strength-based (Basquin-like) and plastic strain – based (Coffin-Manson) power-law relationships, it is appropriate to develop an alloy design philosophy based on either plastic strain energy per cycle (Halford-Morrow) or fatigue toughness (total plastic strain energy to fracture). All of these aspects are discussed in detail in this chapter.

A Criterion for Ductile Fracture in Mild Steels

A criterion of the ductile fracture of mild steels is investigated from the view point of mathematical theory of plasticity.Round bar test specimens are brought to fracture, some under simple tension, some others under simple twist and the rest prestrained under tension and then twisted. The true stress-strain curves at the very point of fracture initiation are carefully examined and correlations between fracture criteria for different stress states are investigated.As the conclusion the criterion is best expressed by the amount of slip energy on the fracture plane. To evaluate the amount of slip energy from a stress-strain curve it is neccessary to make use of the concept of slip theory of plasticity, which constructs plastic strains from integration of infinitesimal slips on every planes. The slip theory is suitable to evaluate the slip energy on any single plane from a stress-strain relation. On the other side another theories of plasticity are not appropriate to distinguish the slip energy on a particular plane from the total plastic strain energy which has no direct relation to the ductile fracture.

Cyclic Plastic Strain Energy and Low-Cycle Fatigue Strength of Nickel-Chrome Steel

Low-cycle fatigue strength of nickel-chrome steel under various cyclic loading conditions, such as constant strain cycling, constant load cycling with and without mean stress, was discussed in relation to the cyclic plastic strain energy. Main results obtained were as follows : (1) The lowcycle fatigue strength depends on the maximum tensile stress σmax as well as on the cyclic plastic strain energy ; (2) in the case of fatigue-type fracture, a unique relation-ship was found between the maximum tensile stress and the cumulative plastic strain energy to fracture, while in the case of unstable deformation-type fracture, another unique relationship existed between the unstable stress and the total plastic strain energy to the initiation of the cyclic unstable deformation. These relations are approximately shown by two straight lines in a log-log diagram. The line of unstable deformation-type failure lies considerably lower than the extrapolated part of the line of fatigue-type fracture.

Low Cycle Fatigue Evaluation of Inconel 713C and Waspaloy

Completely reversed axial fatigue results are reported for Waspaloy and Inconel 713C at room temperature. Fatigue strength and ductility are evaluated using power functions of the fatigue life. The exponents and coefficients of these two equations are looked upon as four fatigue properties of the material. They appear in the equations which are developed to relate cyclic stress, plastic strain, total strain, plastic strain energy per cycle, total plastic strain energy to fracture, and fatigue life. These equations and the four fatigue properties permit the evaluation of the relative fatigue resistance of various metals at different fatigue lives when subjected to strain, stress, or plastic strain energy cycling. The “best” selection of material to resist fatigue is found to depend on the type of cycling and the desired life. At room temperature, the wrought Waspaloy is found to be more fatigue resistant than the cast Inconel 713C, particularly in resisting strain or plastic strain energy cycling in the low cycle fatigue region. For longer lives the difference in fatigue resistance between the two diminishes, especially for stress cycling. It is believed that the method of fatigue evaluation used here is generally applicable to the engineering problem of material selection to resist fatigue, and should in some cases replace methods based on conventional rotating bending fatigue tests which only evaluate the fatigue strength at long lives.