Distortional Strain Energy Research Articles

Suzuki segregation behavior and mechanism in a Co–Cr–Fe–Ni–Mo high-entropy alloy

The knowledge of the Suzuki effect in compositionally complex CoNiCrMo and CoCrFeNiMo solid-solution alloys is rather limited. In this study, the enrichment of Co and Mo atoms and depletion of Cr, Fe, and Ni atoms were determined within the region of four atomic layers at stacking faults (SFs) in a typical quinary concentrated solid-solution alloy (Co0.95Cr0.8Fe0.25Ni1.8Mo0.475) by using scanning transmission electron microscopy and energy dispersive X-ray spectroscopy. To better understand the Suzuki effect, two-stage first-principles Monte Carlo (MC) simulations each with up to 3000 trial swap steps were performed. First, the simulation results suggested the strong tendency of Mo segregation at the second nearest neighbor (2NN) sites at SFs. Nonetheless, as a further Mo segregation induces the excessively large lattice distortion and intrinsic strain energy, it would be inhibited. It was deemed one potential reason for the finite Mo segregation. Second, the simulations revealed the origin and formation of co-segregation of Co and Mo atoms. The segregated Mo atoms at the 2NN sites attract Co atoms, forming the local D019-type ordering at SFs. As a consequence, the stacking fault energy can reach a strongly negative value below −500 mJ/m2. Meanwhile, the Co/Mo co-segregated SFs have high stability against phase transitions to intermetallics and martensite at 773 K.

The effect of dilatational and distortional strain energy density on crack initiation

AbstractTo investigate the distinct influences of dilatational strain energy density (Dil‐SED) and distortional strain energy density (Dis‐SED) on crack initiation, quasi‐static loading tests were performed on centrally cracked polymethyl methacrylate samples, employing digital image correlation equipment. Our findings unveiled that the Dil‐SED promotes crack initiation, while the Dis‐SED inhibits it. Additionally, it was found that the direction obtained by the ratio of these two strain energy densities was closer to the crack initiation direction than the direction associated with the maximum Dil‐SED and minimum Dis‐SED values. Furthermore, experimental and finite element method (FEM) results indicated that the distribution of these two strain energy densities remains relatively insensitive to the core region's radius . By understanding Dil‐SED and Dis‐SED magnitudes and their impacts on crack initiation, material failure can be predicted and prevented.

A modified 3D mean strain energy density criterion for predicting shale mixed-mode I/III fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing. The edge-notched disk bending (ENDB) specimens are employed to measure the entire range of mixed-mode I/III fracture toughness of Longmaxi shale. To theoretically interpret the fracture mechanisms, this research first introduces the detailed derivations of three established fracture criteria. By distinguishing the volumetric and distortional strain energy densities, an improved three-dimensional mean strain energy density (MSED) criterion is proposed. As the critical volumetric to distortional MSED ratio decreases, the transition from tension-dominated fracture to shear-dominated fracture is observed. Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I (i.e., tension) to pure mode III (i.e., torsion or tearing) since mode-III cracking happens in a twisted manner and mode-I cracking occurs in a coplanar manner. The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing. The average ratio of pure mode-III fracture toughness to pure mode-I fracture toughness is 0.68, indicating that the obtained mode-III fracture resistance for a tension-based loading system is apparent rather than true. Compared to the three mainstream fracture criteria, the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-mode I/III fracture toughness of distinct materials and loading methods.

Nonlinear strain energy based (NSEB) criterion for quasi-brittle materials under multiaxial stress states

An equivalent-failure plane model is developed to accommodate the macro-failure phenomenon of quasi-brittle materials under multiaxial stress states. On this basis, strain energy based (SEB) criterion is proposed based on the comprehensive and systematic analysis of strain energy release and dissipation as well as inhibition and acceleration from the normal stress and material itself. In the SEB criterion, the strain energy release is controlled by part of distortional and volumetric strain energy in the block, strain energy dissipation is a function of distortional strain energy, the work of inhibition or acceleration is described as strain energy of normal stress, and the inhibition of materials itself is part of critical shear and cleavage energy density in the block. Then, a nonlinear strain energy based (NSEB) criterion is developed by considering the impact of normal stress on inhibited or accelerated parameters. The NSEB criterion is adopted to predict the multiaxial failure and yield stress of different quasi-brittle materials. The results indicate that the NSEB criterion can predict multiaxial failure and yield stress successfully. Further research indicates that predicted parameters not only are located in the pre-specified range, but also can manifest the micro/meso-experimental phenomenon of different quasi-brittle materials failure. For the purpose of comparison, Hsieh-Ting-Chen, Parabolic Mogi and Bresler-Pister criteria are used to predict the multiaxial failure and yield stress. It can be found that the NSEB criterion gives a better prediction than Hsieh-Ting-Chen, Parabolic Mogi and Bresler-Pister criteria. The determination coefficients R2 of these criteria are also determined. It is noted that the NSEB criterion has a maximum R2 compared with other criteria. Therefore, it is concluded that the NSEB criterion can give a more reliable prediction for multiaxial failure and yield of quasi-brittle materials.

Dynamic Tensile Behavior of Woven C/SiC Composite: Experiments and Strain-Rate-Dependent Yield Criterion.

This paper studies the yield behavior of a woven carbon-fiber-reinforced silicon-matrix (C/SiC) composite under dynamic tensile loading. Experiments were carried out to obtain the tensile properties of the C/SiC composite at a strain rate range of 2 × 10−5/s to 99.4/s. A strain-rate-dependent yield criterion based on the distortional strain energy density theory is established to describe the yield behavior. The interval uncertainty is considered for a more reliable yield prediction. Experimental results show that the yield stress, elastic modulus, and yield strain of the C/SiC composite grow with the increasing strain rate. The failure mode transitions from progressive crack extension to uneven fiber bundle breakage. The predicted results by the yield criterion match well with experimental data. Experimental results are enveloped within the uncertainty level of 45% in the critical distortional energy density, corresponding to an uncertainty of 14% and 11% in the yield stress and yield strain, respectively. With the support of the proposed strain-rate-dependent yield criterion, the yield behavior of the C/SiC composite under dynamic loading conditions can be predicted with reasonable accuracy.

Effect of confining pressures on transverse isotropy of Maha Sarakham salt

Uniaxial and triaxial compression tests have been performed on prismatic specimens of rock salt under confining pressures (σ3) up to 40 MPa. The specimens contain different bedding plane orientations with respect to the major axis. Results indicate that transverse isotropic effects occur under low confinement where the salt strength is lowest when the normal to bedding planes makes an angle (β) of 60° with the major principal axis. The lowest intrinsic elastic modulus is obtained at β = 0°, and the highest is at β = 90°. The apparent elastic parameters measured for 0° < β < 90° agree well with those predicted by Amadei's solutions. The confining pressures rapidly increase the elastic and shear moduli normal to bedding plane strike, and eventually they reach those parallel to the bedding planes under σ3 about 30 MPa. Loading the salt under high confinement induces some plastic deformation, as evidenced by the evolution of Ramberg and Osgood's parameters with the confining pressures. The confining pressures gradually tighten the inter-crystalline boundaries along bedding planes, and hence the applied differential stress can no longer recognize their transverse isotropic textures. The salt strengths for all bedding orientations become equal under σ3 above 30 MPa. The proposed exponential equation is capable of describing the salt dilations and strengths under unconfined to highly confined conditions. Distortional strain energy (Wd) induced at dilation linearly increases with mean strain energy (Wm). The Wd-Wm relation for β = 60° can represent the dilation of the salt from low to high confinements where the mechanical responses of the rock transitionally change from transverse isotropic to isotropic behavior. The Wd-Wm relations for β ≠ 60° are applicable only for confining pressures less than 30 MPa.

ON ESTIMATING PLASTIC ZONES AND PROPAGATION ANGLES FOR MIXED MODE I/II CRACKS CONSIDERING FRACTAL EFFECT

This paper mainly investigated the influence of the fractal dimension of mixed mode I/II crack on its near-tip plastic zones and propagation angles. The near-tip distortional strain energy density for mixed mode I/II crack is modified by considering its fractal dimension. Using the Von Mises yield condition, the plastic zones at the fractal crack tip are evaluated. The effects of the fractal dimension of crack on the near-tip plastic zones are analyzed qualitatively. A modified criterion minimizes the fractal distortional strain energy density to predict the propagation direction of mixed mode I/II crack. Based on this, the effects of fractal dimension on the mixed mode I/II crack propagation direction at different inclination angles are discussed quantitatively. In addition, the modified criterion is compared to the experimental data in the literature, as well as the classical maximum tangential stress criterion and minimum strain energy density criterion. The results indicate that the fractal dimension of crack is an important factor in evaluating the crack-tip plastic zones and predicting the crack propagation angle, and the modified fractal criterion is more accurate and effective in predicting the crack propagation angles.

Determination of equivalent axle load factors with the use of strain energy of distortion

The paper proposes a new method for calculation of equivalent axle load factors based on the analysis of strain energy of distortion induced in road pavements by traffic loads. The main advantage of the method is the more accurate calculation of the effects of multiple axles and super single versus dual tyres. The methodconsiders the location of critical points, at which strain energy of distortion reaches extreme values. When single axles are considered, the function of equivalent axle load factor takes on the form of the well-known power equation with the exponent ranging from 2.7 to 5.3. It was proved that the damaging effect of triple axles on asphalt pavement is several times higher than the damaging effect of three single axles carrying the same load, but at a greater distance to each other. Due to this fact, traffic load may be significantly underestimated in many pavement design methods.

Spalling prediction by distortion strain energy

Spalling can be a serious threat to underground excavation works in hard, good quality rock masses at great depth. Spalling endangers drill & blast advance or TBM drives with severe damage of tunnel walls or the face. In mining the concern is about spalling at pillars and at the face. Research on spalling is mainly associated with the definition of Crack Initiation (CI) and Crack Damage (CD) stresses and the definition of the S-shaped spalling strength envelope. Particularly CI stress at low confining stress (σcc/σ3 < 0.05 and σ1/σ3 < 10) is important for defining spalling around an underground excavation in hard rock. We summarize 59 UCS tests and 197 triaxial tests (σ3 < 2.5 MPa) with sedimentary, magmatic, and metamorphic rocks, respectively, and defined robust CI and CD stresses. In this paper, we focus on the distortional strain energy at CI and CD stresses. From a rock mechanical point of view, crack initiation and crack damage are associated with stress (or strain) deviation. Analyses of the very well instrumented tests shows that for any rock type (saturated and dry) crack initiation (CI) occurs at 20% and crack damage (CD) at 75% of the distortion strain energy at failure. This approach was tested at the well-known case of spalling at the test tunnel in the AECL Underground Research Laboratory. Mechanical properties for the Lac du Bonnet granite were used to estimate distortional energy at CI and to model breakout depth and shape.

Modified Johnson-Cook constitutive model of metallic materials under a wide range of temperatures and strain rates

This study concentrated on presenting the classical Johnson-Cook model by introducing a new temperature term, under the framework of an equivalence between heat energy and distortional strain energy. Importantly, the inner relationship among temperature, elastic modulus, the specific heat capacity at constant pressure, and Poisson's ratio was established quantitatively. What the nicest character this term had was that there were no fitting parameters, which made the model be applicable when the temperature was lower than the reference temperature. Thus, the improved Johnson-Cook model could effectively predict the mechanical behavior over a wide range of strain rates and temperatures. Using sets of experimental data with varying temperatures and strain rates, a multi-objective approach combined with the Latin hypercube sampling method, Spearman rank correlation analysis, and an advanced genetic algorithm, was applied for the constitutive model parameter identification and optimization. Consequently, the stress-strain responses of several metallic materials under various complex conditions were reproduced by the proposed model. It was shown that there was a good agreement between the prediction and experiment results, even though the temperature was lower than the reference temperature.

In situ and tunable structuring of semiconductor-in-glass transparent composite.

SummarySemiconductor-in-glass composites are an exciting class of photonic materials for various fundamental applications. The significant challenge is the scalable elaboration of composite with the desirable combination of tunable structure, high semiconductor loading ratio, and excellent transparency. Here we report that the topological engineering strategy via hybridization of the glass network former enables to surmount the aforementioned challenge. It not only facilitates the in situ precipitation of (Ga2-xAlx)O3 domains with continuously tunable composition but also allows to simultaneously refine the grain size and enhance the crystallinity. In addition, the composites exhibit excellent transparency and can host various active dopants. We demonstrate the attractive broadband optical response of the composite and achieve the pulse laser operation in mid-infrared waveband. The findings are expected to provide a fundamental principle of in situ modification in hybrid system for generation of high-performance semiconductor-in-glass composites.

A Discrete Fracture Network Model With Stress-Driven Nucleation: Impact on Clustering, Connectivity, and Topology

The realism of Discrete Fracture Network (DFN) models relies on the spatial organization of fractures, which is not issued by purely stochastic DFN models. In this study, we introduce correlations between fractures by enhancing the genetic model (UFM) of Davy et al. [1] based on simplified concepts of nucleation, growth and arrest with hierarchical rules. To do so, the nucleation of new fractures is correlated with the elastic strain energy of distortion stored in the matrix, which is a function of preexisting fractures. Discrete Fracture Networks so generated show multi-scale clustering effects with fractal dimensions below the topological dimension over a broad range of scales. The fractal dimension depends on the way one correlates the nucleation occurrence to the strain energy. Fracture clustering entails a spatial variability of the fracture density, which increases with the intensity of the coupling between stress and nucleation. The analysis of connected clusters density and of fracture intersections also highlights the differences between the UFM models and its equivalent Poisson model. We show that our stress-dependent nucleation model introduces some new fracture size-positions correlations, with small fractures tending to connect to the largest ones.

An Innovative Yield Criterion Considering Strain Rates Based on Von Mises Stress

Abstract An innovative yield criterion based on von Mises stress is proposed to represent the strain rate-dependent behavior under dynamic load. Considering the strain rate in the constitutive model, the distortional strain energy density is derived and the yield criterion is established. A plot of yield strength for a range of strain rate reveals that despite the differences in material properties and test methods, the yield strength rise can be represented by a unified criterion. The overall yield behavior of the material under dynamic load can be explained by introducing the strain rate into the constitutive model and threshold distortional strain energy density. This criterion is in a simple form that may be widely applied.

Análisis por elementos finitos del desempeño estructural de jaula de seguridad para vehículo Renault Logan bajo normatividad FIA

Este artículo presenta el análisis estructural de una jaula de seguridad para Renault Logan 2005 bajo la normatividad de la Federación Internacional de Automovilismo para vehículos de turismo; particularmente, se considera el ensayo de carga vertical sobre el arco principal. Se llevaron a cabo simulaciones por medio de un software de elementos finitos, en las cuales se definieron la geometría y material usado, además de establecer las condiciones de frontera, carga y contactos. Se analizó el comportamiento mecánico bajo la carga exigida por FIA de 90 KN teniendo en cuenta el criterio de falla de la energía de distorsión y la deformación total. Posteriormente, se encontró que deformaciones permanentes pueden originarse por encima de 32.2 KN, mientras que fallas localizadas pueden presentarse por encima de 44 KN. Hay que mencionar además que los resultados demuestran que la implementación de las exigencias mínimas geométricas, de material y de manufactura de FIA no garantizan necesariamente la seguridad de la estructura.

Stress optimization of smooth continuum structures based on the distortion strain energy density

This paper presents an evolutionary structural optimization method of designing continuum structures with clear and smooth boundaries for stress minimization. The stress optimization problem is formulated with the P-norm function based on the distortion strain energy density, so as to avoid the stress relaxation and the local nature of the maximum stress. In order to obtain a smooth topology, the surrogate design variables on the volume fraction of elements are defined based on the proportion of solid and void points within an element. Based on sensitivity analysis, topology optimization evolves the structure by gradually decreasing the structural volume to the optimized one with the prescribed volume. 2D and 3D numerical examples are presented and discussed to demonstrate the effectiveness of the proposed topology optimization method for minimizing the maximum stress of continuum structures and alleviating stress concentration.

Thermal effects on shearing resistance of fractures in Tak granite

Triaxial shear tests have been performed on tension-induced fractures and smooth saw-cut surfaces in Tak granite under temperatures up to 773 K. The objective is to gain an understanding of the movement of shallow faults that cause seismic activities in the Tak batholith in the north of Thailand. The results indicate that the peak and residual shear strengths and fracture dilations notably decrease as the temperatures increase. The thermal effect is enhanced under higher confining pressures. The areas of the sheared-off asperities increase with temperature and confining pressure. A power equation can describe the increase of shear strengths with normal stress where the normal stress exponent is a linear function of the temperature. The strain energy principle is applied to incorporate the principal stresses and strains into a strength criterion. A linear relation between the distortional strain energy (Wd) and the mean strain energy (Wm) of the fractures is obtained. The Wd-Wm slope depends on the fracture roughness and strength of the asperities, which can be defined as a function of shear and mean strains and dilation of the fractures. This may allow predicting the peak strength of the shallow faults in the Tak batholith.

The low-cycle fatigue life assessment method for online monitoring of steam turbine rotors

The paper presents a simple method for the low-cycle fatigue life monitoring of steam turbine rotors. The method makes use of the equivalent strain energy density rule of notch stress-strain analysis proposed by Molski and Glinka. The method is applied to low-cycle fatigue analyses of steam turbine rotors operating at non-isothermal conditions. A strain energy correction factor is introduced to include the distortion strain energy density. Assessment of the proposed method was done by comparing their estimations with the strain amplitudes obtained from the finite element analysis employing elasitc-plastic material model. The inclusion of energy correction factor obtained from the elastic-plastic finite element analysis significantly improves the accuracy of strain amplitudes and fatigue life estimations. The strain calculation algorithm is based on an analytical solution of the equivalent strain energy equation what makes it very useful for real time fatigue calculations.

A generalized mean stress correction model based on distortional strain energy

A new fatigue damage model based on the distortional strain energy is presented and discussed to account for the mean stress effects on fatigue life. The proposed model is compared to the Morrow and the SWT mean stress correction models using experimental mean stress fatigue data for Incoloy 901 superalloy, 120–90-02 ductile cast iron and 7075-T651 aluminum alloy under tensile and compressive mean stress loadings. The proposed model and the SWT model are found to show similar fatigue predictions and show good agreement for positive mean stress data and moderate negative mean stress data. The proposed model shows reasonably good agreement while the SWT model is unable to correlate mean stress data under large compressive mean stress conditions. The Morrow model provides poor correlations for all fatigue data analyzed by yielding conservative results for compressive mean stresses and non-conservative results for tensile mean stresses.

Fracture behaviour at the sharp notch tip of high strength rail steels – Influence of stress triaxiality

This work explores the possibility of using mechanical properties of two types of notch-free specimens to evaluate crack growth resistance of a sharp notch tip. Equivalent plastic fracture strain (εeqf,ηav) of pre-cracked single-edged-notched bending (SENB) specimen is estimated using a model that correlates εeqf,ηav for notch-free specimens with their average stress triaxiality. Finite element modelling is used to establish constitutive equations and variations of stress triaxiality in the two types of notch-free specimens and the pre-cracked SENB specimen. All of the information is then used to predict the critical strain energy density factor (Sc) at a characteristic distance ahead of the sharp notch tip and the corresponding stress intensity factor (KSc) for three high strength rail steels. The predicted KSc values are compared with the experimentally measured mode I critical stress intensity factor (KIc) at temperatures 23, −10, and −40°C. The results show good agreement between KSc and KIc in their variation with temperature, possibly because Sc takes into account both distortional and dilatational strain energy density of the sharp notch tip under small-scale yielding. Results from the study also suggest that a correlation should exist among mechanical properties for notch-free and notched specimens, though their apparent trend of change with temperature may not bear any similarity.

Distortion Strain Energy–Based Mohr-Coulomb Criterion for Concrete Failure

AbstractOn the basis of comprehensive analysis of experimental phenomenon and micro/mesomechanism, it is found that concrete failure is controlled by normal stress on failure plane and distortion s...