Strain Energy Density Factor Approach Research Articles

Theoretical optimization of micropillar arrays for structurally stable bioinspired dry adhesives

Inspired by the excellent adhesion performances of setae structure from organisms, micro/nano-pillar array has become one of the paradigms for adhesive surfaces. The micropillar arrays are composed of the resin pillars for adhesion and the substrate with different elastic modulus for supporting. The stress singularity at the bi-material corner between the pillars and the substrate can induce the failure of the micropillar-substrate corner and further hinder the fabrication and application of micropillar arrays, yet the design for the stability of the micropillar array lacks systematical and quantitative guides. In this work, we develop a semi-analytical method to provide the full expressions for the stress distribution within the bi-material corner combining analytical derivations and numerical calculations. The predictions for the stress within the singularity field can be obtained based on the full expressions of the stress. The good agreement between the predictions and the FEM results demonstrates the high reliability of our method. By adopting the strain energy density factor approach, the stability of the pillar-substrate corner is assessed by predicting the failure at the corner. For the elastic mismatch between the pillar and substrate given in this paper, the stability can be improved by increasing the ratio of the shear modulus of the substrate to that of the micropillar. Our study provides accurate predictions for the stress distribution at the bi-material corner and can guide the optimization of material combinations of the pillars and the substrate for more stable bioinspired dry adhesives.

The micromechanics‐based rate‐dependent constitutive model of flawed rocks at intermediate strain rate

AbstractIn the previous works conducted by Zhou and Yang, the deformation induced by wing crack coalescence was not investigated. In this paper, a novel micromechanics‐based rate‐dependent constitutive model is proposed to investigate the effect of wing crack coalescence on the mechanical properties of rocks at intermediate strain rate. The rate‐dependent damage mechanism is revealed using the frictional sliding crack model. Wing crack interaction is defined using pseudo‐traction method as well as the dynamic stress intensity factors. Strain energy density factor approach is applied to determine the critical condition of wing crack initiation, propagation, and coalescence. The strain softening behaviors of flawed rocks is studied by using thermodynamic theory.

Dynamic damage localization in crack-weakened rock mass: Strain energy density factor approach

The key failure mechanism of rock mass subjected to compressive loads is due to the damage localization. Conventional methods can not be applied to study the dynamic damage localization physical behavior of crack-weakened rock mass. The strain energy method has the capability to investigate the dynamic damage localization feature in crack-weakened rock mass. Therefore, in order to analyze the dynamic damage localization behavior, strain energy density factor approach is adopted in this paper. A two-dimensional model with periodic rectangular noncollinear array of cracks is established. Then, the onset condition of periodic distribution cracks in rock mass is obtained using strain energy density factor approach. By analyzing the bifurcation of crack growth pattern, the critical length and stress of damage localization of crack-weakened rock mass is determined as well as the location of damage localization. In addition, parameters sensitivity analysis is carried out, the effects of the length of crack, friction coefficient, fracture toughness, confining stress, velocity of crack growth, inclination and spacing between lines and rows on the onset condition for damage localization and bifurcation pattern of rocks are discussed. It can be concluded that onset condition of damage localization is mainly affected by its distribution of initial cracks.

Dynamic damage constitutive relation of mesoscopic heterogenous brittle rock under rotation of principal stress axes

A micro-mechanics-based model is developed to investigate microcrack damage mechanism of four stages of brittle rock under rotation of the principal stress axes. They consist of linear elastic, non-linear hardening, rapid stress drop and strain softening. The frictional sliding crack model is applied to analyze microcracks nucleation, propagation and coalescence. The strain energy density factor approach is applied to determine the critical condition of microcrack nucleation, propagation and coalescence. The inelastic strain increments are formulated within the framework of thermodynamics with internal variables. Rotation of principal stress axes affect the dynamic damage constitutive relationship and the failure strength of brittle rock.

Reliability assessment of a bi-material notch: Strain energy density factor approach

Joints of different materials have many applications in structural engineering and microelectronics. In the present contribution the joint is modelled as a bi-material notch. The singular stress field near the notch tip is investigated. Depending on the notch geometry and materials, the stress field can have one or two singularities. It is shown that to study the problem of a crack onset at the notch, both terms have to be taken into account. Criteria for the direction and for crack nucleation are formulated. The approach utilizes the knowledge of the strain energy density factor distribution in a bi-material notch vicinity.

Micromechanical modeling of dynamic compressive responses of mesoscopic heterogenous brittle rock

A micromechanical model is developed to investigate microcrack damage mechanism and shear localization of brittle rock subjected to dynamic compressive loads, in which the probability density function describing the distribution of orientations and sizes is assumed to follow the Weibull distribution. To investigate microcracks nucleation and propagation and coalescence, a frictional sliding crack model and the strain energy density factor approach, which is related to crack growth velocity and dynamic fracture toughness of rock material, are applied to provide important insights into how different attributes of the microstructure and strain rate may influence the progressive development of rock shear failure subjected to dynamic compressive loads. It is verified from numerical results that the effect of strain rate on fracture strength of brittle rock is independent of confinement pressure in a certain range of strain rate. The microstructural data indicate that strength heterogeneity increases with an increase in the length of crack, strength decreases with increasing the length of crack.

Mixed-Mode Fatigue Crack Growth in Orthotropic Steel Decks

The strain energy density factor approach under mixed-mode condition is used for the prediction of crack propagation in the orthotropic steel deck specimen, which is similar to that of existing suspension bridges. Stress intensity factor approach is used to compare with strain energy density factor approach for the fatigue crack growth analysis. The stress intensity factors are computed by numerical extrapolation using cracked models for the different crack length. The study shows that the fatigue crack propagation under mixed-mode condition is slower than that under mode I only. Parametric studies on the initial crack length, critical crack length and parameters related to crack growth equations are performed to show the influence of these parameters on the fatigue life.

Upper and lower bounds for constitutive relation of crack-weakened rock masses under dynamic compressive loads

A micro-mechanics-based model is proposed to investigate the rate-dependent constitutive relation for crack-weakened rock masses subjected to dynamic compressive loads. The present micro-mechanical model reveals that the nucleation, growth and coalescence of sliding cracks dominate the failure and macroscopic properties of crack-weakened rock masses subjected to dynamic compressive loads. The interactions among multiple parallel sliding cracks in crack-weakened rock masses subjected to dynamic compressive loads are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the stress–strain relation. Based on the micro-mechanical framework and the asymptotic analysis, analytical upper and lower bounds are proposed for the rate-relation for rock masses containing multiple rows of echelon cracks subjected to dynamic compressive loads. The factors that affect the rate-dependent properties of crack-weakened rock masses have been analyzed. The strain energy density factor approach, which is related to crack growth velocity and dynamic fracture toughness of rock material, is employed in the analysis. The rate-dependent constitutive relation of crack-weakened rock masses is derived from micro-mechanical framework and the asymptotic analysis. The closed-form explicit expression for the rate-dependent constitutive relation of rock masses containing echelon cracks subjected to dynamic compressive loads is obtained. Finally, the present model is used to analyze the complete stress–strain relation and strength for jointed rock masses at shiplock slope of the Three Gorges Dam.

Fatigue life prediction of in-plane gusset welded joints using strain energy density factor approach

Fatigue crack growth behavior of in-plane gusset welded joints is studied using the strain energy density factor approach. Fatigue tests were performed in order to estimate fatigue strength under tension. Fatigue crack growth analysis was carried out to show the effects of the initial crack shape, the initial crack length, and the stress ratio on the crack types of in-plane gusset welded joints. The assumed crack types were edge crack, semi-elliptical crack, and corner crack. Fatigue crack growth parameters were obtained from crack growth curves assuming constant crack shapes for the given crack types. The results of analysis for the assumed crack types agreed well with the experimental data. The fatigue life did not change as initial crack shape varied for a given initial crack length.

Triaxial compressive behavior of rock with mesoscopic heterogenous behavior: Strain energy density factor approach

The strain energy density factor approach is used in conjunction with a micromechanics model to investigate the condition and direction of shear failure for brittle rock subjected to triaxial compression. Moderate confinement in addition to localized deformation and damage are considered. Quantified are the effects of the various geometric and load parameters that involve the interaction of microcrack, friction and the confining pressure such that the path of the wing crack is taken into account. The influence of all microcracks with different orientations are introduced into the constitutive relation. The closed-form solution for the complete stress–strain relation of rock containing microcracks is obtained. It is shown that the complete stress–strain relationship includes linear, nonlinear hardening, rapid stress drop and strain softening effects. The theoretical results show that deviation of the direction of wing cracks from the line of the pre-existing crack decreases with increasing confinement pressure and friction coefficient. Theoretical predictions and experimental results show good agreement.

Fatigue crack growth with overload under spectrum loading

Load cycle interactions can have a very significant effect in fatigue crack growth under variable amplitude loading. Studying of fatigue crack growth rate and fatigue life calculation under spectrum loading is very important for the reliable life prediction of engineering structures. In this paper, a fatigue life prediction model under various load spectra, using the strain energy density factor approach and the plastic zone size near crack tip as main parameters in calculating effective strain energy density factor, has been proposed. The present model is validated with fatigue crack growth test data provided by Ray under various variable amplitude and spectrum loading in 7075-T6 and 2024-T3 aluminum alloy, respectively. Predictions of present model are compared with those of the state-space model, FASTRN and AFGROW codes. The results show that the predicted results agree well with the test data.

Fatigue life prediction of out-of-plane gusset welded joints using strain energy density factor approach

Fatigue growth behavior of out-of-plane gusset welded joints is studied using the strain energy density factor approach. Fatigue tests on two types of specimens with curvatures of ρ = 0 and ρ = 30 were performed in order to estimate fatigue strength under tension. Fatigue crack growth analysis is carried out to show the effects of initial crack shape, initial crack length and stress ratio. Fatigue crack growth parameters were obtained from crack growth curves assuming constant crack shapes. The results of analysis for the assumed crack shapes agreed well with the experimental data. Fatigue propagation life of the ρ = 30 specimen was larger than that of the ρ = 0 specimen.

Fatigue life prediction of welded cruciform joints using strain energy density factor approach

The influences of two welding processes, namely, shielded metal arc welding (SMAW) and flux cored arc welding (FCAW), on fatigue life of cruciform joints containing lack of penetration (LOP) defects have been analyzed by using the strain energy density factor (SEDF) approach. Load carrying cruciform joints were fabricated from ASTM 517 ‘F’ grade steel. Fatigue crack growth experiments were carried out in a mechanical resonance vertical pulsator (SCHENCK 200 kN capacity) with a frequency of 30 Hz under constant amplitude loading ( R=0). It was found that the fatigue lives of the cruciform joints fabricated by SMAW process were relatively higher than the FCAW counterpart. Moreover, fracture mechanics equations have been developed to predict the fatigue life of the cruciform joints fabricated by the above-mentioned two processes.

Effect of weld size on fatigue crack growth behaviour of cruciform joints by strain energy density factor approach

The effect of weld size on fatigue crack growth behaviour of cruciform joints containing lack of penetration defect has been analysed by using the strain energy density factor concept. Load carrying cruciform joints were fabricated from ASTM 517`F' grade steel. Fatigue crack growth experiments were carried out in a mechanical resonance vertical pulsator (SCHENCK 200 kN capacity) with a frequency of 30 Hz under constant amplitude loading ( R=0). It was found that the crack growth rates were relatively lower in the larger welds fabricated by multipass welding technique than the smaller welds fabricated by the single pass welding technique.

Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.