The effect of repeated high-pressure hydrogen cycles on the decompression failure of unfilled EPDM was investigated from in-situ images of the damage field during decompression. The purpose was to characterize the relative influence of some parameters of the pressure cycle (decompression rate, residual pressure and time between two cycles) and to investigate damage cumulative features. Beyond that, the aim of this wide range of decompression conditions was to separately vary the external pressure and gas diffusion histories, in order to discuss them as driving force contributions to damage growth. Such extended decompression conditions confirmed coupled contributions of diffusion and mechanics. Exposure conditions allowing a significant part of gas diffusion promoted clustering and later macro-cracking, provided that the residual external pressure was low enough. A more heterogeneous spatial distribution of damage was also observed, within clusters and at the sample scale, with non-trivial re-opening of cavities from one cycle to another. More restrictive exposure conditions (i.e., limited diffusion times or residual external pressure) reduced or prevented the onset of cavities, clustering and transition to macro-cracking. More homogeneous damage fields were observed, along with more systematic re-appearing and growth of the same defects with cycling. Damage processes appeared more spatially confined.

This article presents the results of an investigation of crack nucleation and propagation in a transparent polydimenthylsiloxane (PDMS) elastomer. The main objective of the investigation is to characterize quantitatively the evolution of crack nucleation and propagation behavior not just through the usual macroscopic load and displacement data, but with synchronized optical images at high spatial and adequate temporal resolution that will resolve the evolution of the failure processes. This is augmented with X-ray computed tomography (CT) scans to characterize the three-dimensional geometry of the cracks nucleated in the interior of the elastomer. Towards this goal, we reproduce the classical poker-chip experiment of Gent and Lindley (Proc R Soc Lond A 249(1257):195–205, 1959) in which the specimen’s diameter-to-thickness ratio is varied over a broad range to cover crack nucleation, propagation, and their coalescence. These experiments are performed on transparent PDMS with different compositions, first in a specially built loading machine that is fitted with a high magnification microscopic camera that permits the measurement of the load while simultaneously providing images of the specimen configuration and subsequently in an apparatus built for in situ observations using an X-ray CT scanning system. These experiments reveal that nucleation of multiple microcracks dominates when the diameter-to-thickness aspect ratio \(\alpha \) is sufficiently large, because the incompressibility of the material induces substantial, nearly uniform hydrostatic tension in the specimen. In contrast, specimens with smaller aspect ratio tend to nucleate fewer cracks, and are dominated by the growth of these cracks. At even smaller \(\alpha \), the hydrostatic stress is significantly lowered and failure is dominated by surface flaws. The three-dimensional geometry, and the spatial distribution of the nucleated cracks were evaluated using optical microscopy and X-ray CT scans. This revealed cracks of three different shapes, one of which was confined in a layer near to the upper or bottom boundary of the poker-chip, another was across the thickness, but with a tilt relative to the axis of the specimen, and the last was propagating along the radial direction.

In this work, two non-local approaches to dynamic fracture are investigated: a novel peridynamic formulation and a variational phase-field approach. The chosen continuum-kinematics-based peridynamic model extends the current peridynamic models by introducing surface and volume-based interactions. The phase-field fracture approach optimizes the body’s potential energy and provides a reliable method for predicting fracture in finite element computations. Both methods are able to efficiently compute crack propagation even when the cracks have arbitrary or complex patterns. We discuss the relations of critical fracture parameters in the two methods and show that our novel damage model for the continuum-kinematics-based peridynamics effectively manages fracture under dynamic loading conditions. Numerical examples demonstrate a good agreement between both methods in terms of crack propagation, fracture pattern, and in part, critical loading. We also show the limitations of the methods and discuss possible reasons for deviations.

The size and viscosity effects are noticeable at the micro-/nano scale. In the present work, the strain gradient viscoelastic solution of the mode-III crack in an infinite quasi-brittle advanced material is proposed based on the strain gradient viscoelasticity theory using the Wiener–Hopf method. The solutions to the gradient-dependent viscoelastic crack problem are obtained directly by using the correspondence principle between the strain gradient viscoelasticity and strain gradient elasticity in Maxwell’s standard linear solid model. In this model, the stress near the crack tip is time-dependent and size-dependent. Besides, the stress near the crack tip is more significant than that based on gradient elasticity theory. Compared with the elastic strain gradient effect, the viscous gradient effect makes the stress field at the crack tip harden. The location and the value of maximum stress change with time, which differs from the case in strain gradient elasticity theory. The time that the normalized stress takes to stabilize also changes with the distance from the crack tip. When the viscosity effect is neglected or time tends to infinity, the strain gradient viscoelasticity theory can be reduced to the classical strain gradient elasticity theory.

In this work, the essential work of fracture (EWF) method is introduced for a peridynamic (PD) material model to characterize fracture toughness of ductile materials. First, an analytical derivation for the path-independence of the PD J-integral is provided. Thereafter, the classical J-integral and PD J-integral are computed on a number of analytical crack problems, for subsequent investigation on how it performs under large scale yielding of thin sheets. To represent a highly nonlinear elastic behavior, a new adaptive bond stiffness calibration and a modified bond-damage model with gradual softening are proposed. The model is employed for two different materials: a lower-ductility bainitic-martensitic steel and a higher-ductility bainitic steel. Up to the start of the softening phase, the PD model recovers the experimentally obtained stress–strain response of both materials. Due to the high failure sensitivity on the presence of defects for the lower-ductility material, the PD model could not recover the experimentally obtained EWF values. For the higher-ductility bainitic material, the PD model was able to match very well the experimentally obtained EWF values. Moreover, the J-integral value obtained from the PD model, at the absolute maximum specimen load, matched the corresponding EWF value.

In this paper, the interfacial behavior of a thin two-dimensional decagonal quasicrystal (QC) film bonded on an elastic substrate is investigated due to a material mismatch strain under thermal variation. The non-slipping contact condition is assumed at interface. The Fourier transform technique is used to transfer the problem as an integral equation in terms of the phonon interfacial shear stress, which can be numerically solved by introducing the series expansion of Chebyshev polynomials. The expressions are explicitly presented for the phonon interfacial shear and internal normal stresses, the horizontal displacement of QC film, and the stress intensity factors. In the numerical calculation, the effects of material mismatch, the geometry of QC film, and temperature variation on the stresses, displacement and stress intensity factors are briefly discussed. It is expected that the results will be helpful to the design and safety assessment of a QC film/substrate system in engineering applications.

This paper is a continuation of two recent publications on crack growth in viscoelastic media. It provides further theoretical results for large strains that enable prediction of crack opening displacement for comparison with experimental data in the region of the singularity. In order to achieve good agreement with experiment it was necessary to account for far-field viscoelasticity. Additionally, it is found that with large deformation throughout the singularity, the deformation consists of simple shearing and stretching normal to the crack plane. Thus, there is no significant displacement parallel to the crack plane; such simplicity exists for materials that stiffen or soften at high strains if the stress obeys a power law in strain at high strains. This finding means that, despite the frame-dependence of the theory, there is no local rotation in the singularity to affect the stress.

A weakly singular boundary integral equation (BIE) method is developed for the analysis of T-stresses for cracks in three-dimensional, anisotropic, linearly elastic, finite bodies. A system of BIEs governing unknown data on the boundary and crack-face displacement is developed in a broad framework, allowing for the treatment of material anisotropy, finite boundaries, cracks of arbitrary shape, and general loading conditions. To alleviate the requirement on handling all involved singular integrals, a regularization approach is also used to finally obtain BIEs containing only weakly singular kernels. An efficient solution procedure based on a symmetric Galerkin boundary element method and a Galerkin-based approach is implemented to solve the resulting governing BIEs. The near-front field’s structure is used to enhance the approximation of crack-face displacement and to provide accurate and direct means for calculating the T-stresses from solved sum of the crack-face displacement. The results of a comprehensive numerical study show that the proposed technique is not only accurate but also capable of handling finite cracked bodies under various scenarios.

The complex process of fracture occurring in heterogeneous quasi-brittle material concrete under splitting tensile load is researched using the acoustic emission (AE) and digital imaging tools. Analyses of the AE events and energy reveal four stages of fracture under opening mode—elastic stage, growth of microcracks, stable crack growth and major crack growth until final failure. In the stable crack growth stage simultaneous microcracking and their coalescence into macrocracks take place. The dimensions and shape of the fracture process zone (FPZ) are determined through the distribution of acoustic emission events and their kernel density contours. Assuming a logistic or sigmoid law for the growth of micro and macro cracks, the b-value is seen to increase steadily reaching a constant magnitude close to failure. The growth of logistic b-value is found to follow the crack growth curve indicating its use in predicting failure.

A interaction model between discrete dislocation emission and the grain boundary at the crack tip of microscale grain is described. When the dislocation emission condition is satisfied, dislocations will be emitted from the crack tip and will move along a slip plane to the grain boundary. Dislocations will pile at the grain boundary and create stress concentration. At this time dislocation penetration and crack nucleation at the grain boundary may occur. The distribution and penetration of dislocations at the crack tip will have a new effect on the crack. In this paper, different grain boundary angles and grain sizes are studied to find the relationship between dislocations and cracks. The results show that the main crack tends to propagate in large grain boundary angle and in small grain size crystalline materials. And wedge crack in the grain boundary tends to initiate with large grain boundary angle and in large grain size crystalline materials.

The pore pressure cohesive element was used to simulate the hydraulic fracturing process in layered-fractured-plastic formations. The effects of formation modulus, natural fractures, and formation plasticity on the propagation behaviors of hydraulic fracture were investigated. The results show that the internal stress induced by the incompatible deformation between adjacent formations controls the hydraulic fracture propagation in layered formations. The natural fractures in bounding formation can facilitate the initiation and propagation of hydraulic fracture in fracturing formation, and the connectivity of natural fractures determines the propagation mode of hydraulic fracture (i.e., tensile failure or shear failure). The formation plasticity can inhibit the hydraulic fracture propagation but on the other hand can facilitate its propagation in adjacent formation.

The mechanical properties of metal matrix fiber-reinforced composites depend on many aspects of their structure in a complicated way. In this paper, we propose a phase-field-cohesive-zone framework to study interface debonding, matrix cracking, and their competition in metal matrix fiber-reinforced elastoplastic composites by numerical simulation. This approach combines an explicit cohesive zone model for interface debonding and a phase field model for matrix cracking. The features of this framework are: (1) crack propagation and branching can be simulated without the need to track the cracks; (2) the interface debonding is described by the cohesive zone model, and is not directly interfered by the phase field in the bulk; (3) the cohesive interface has zero thickness instead of being regularized; (4) any reasonable cohesive law of interest is readily incorporated with very few constraints; (5) the competition of the two failure mechanisms, namely, matrix cracking and interface debonding, is captured. Accuracy of this framework is verified with existing analytical and numerical results. The proposed framework shows a potential in investigating various complicated crack behaviors in composites.

Anisotropic elastic materials containing multiple elliptical cracks of different orientation distributions are considered using the (self-consistent) effective field method. The method allows, in particular, accounting for mutual positions of cracks. The derived effective elastic stiffness tensor applies to a broad range of the crack density. Group velocity surfaces (wave surfaces) of cracked materials are constructed. It is shown that, for the isotropic materials with parallel penny shaped cracks, the wave surfaces are close to ellipsoidal. A method of solution of the inverse problem and determination of fracture parameters from acoustical data (group velocities of quasi-longitudinal and quasi-transverse waves of various directions in damaged rock materials) is proposed. Examples of application of the method are presented, and its accuracy is assessed. The results can be used for determination of crack density in rock materials by acoustical methods.

Up to the beginning of the twenty-first century, most of quasi-brittle structures, in particular the ones composed by concrete or masonry frames and walls, were designed and built according to codes that totally ignored fracture mechanics theory. The structural load capacity predicted by strength-based theories, such as plastic analysis and limit analysis, do not exhibit size-effect. Within the framework of fracture mechanics theory, this paper deals with the analysis of the effect of non proportional loadings on the strength reduction with the structural scaling. In particular, this study investigates the size-effect of quasi-brittle materials subjected to self-weight. Although omnipresent, gravity-load is often considered negligible in most studies in the field of fracture mechanics. This assumption is obviously not valid for large structures and in particular for geometries in which the dead load is a major driving force leading to fracture and structural failure. In this study, an analytical formulation expressing the relation between the strength-reduction and the structural scaling and accounting for self-weight, was derived for both notched and unnotched bodies. More specifically, a closed form expression for size and self-weight effects was first derived for notched specimens from equivalent linear elastic fracture mechanics. Next, equivalent linear elastic fracture mechanics theory being not applicable to unnotched bodies, a cohesive model formulation was considered. Particularly, the cohesive size effect curve and the generalized cohesive size effect curves, originally obtained via cohesive crack analysis for weightless bodies with sharp and blunt/unnotched notches, respectively, were equipped of an additional term to account for the effect of gravity. All the resulting formulas were compared with the predictions of numerical simulation resulting from the adoption of the Lattice Discrete Particle Model. The results point out that the analytical formulas match very well the results of the numerical model for both notched and unnotched samples. Furthermore, the analytical formulas predict a vertical asymptote for increasing size, in the typical double-logarithm strength versus structural size representation. The asymptote corresponds to a characteristic size at which the structure fails under its own weight. For large structural sizes approaching this characteristic size, the newly developed formulas deviate significantly from previously proposed size-effect formulas. The practical relevance of this finding was demonstrated by analyzing size and self-weight effect for several quasi-brittle materials such as concrete, wood, limestone and carbon composites. Most importantly, the proposed formulas were applied to the failure of semi-circular masonry arches under spreading supports with different slenderness ratios. Results show that analytical formulas well predict numerical simulations and, above all, that for vaulted structures it is mandatory accounting for the effect of self-weight.

In this paper, we investigate the effects of material damage on mode I crack tip fields near an advancing crack in a neo-Hookean sheet using a phase field model. Phase-field governing equations are introduced and solved using the finite element method combined with a Riks path-following approach, which allows for tracking of non-monotonic evolution of the equilibrium path in a fracture process. We calibrate the scale parameter in the phase field model based on an energy method where the prescribed fracture energy is equal to the real energy dissipation in fracture of a 1D bar. We observe good agreement between the stress-stretch relation of the phase field model and experimental data in tearing of a long notched neo-Hookean strip in multiple loading cases. We find that the crack tip fields are self similar as the crack propagates. Due to material damage, the normal stress component shows a peak value ahead of the crack rather than the singular behavior observed in a purely elastic neo-Hookean material. We show that the magnitude of the peak stress is proportional to the critical fracture energy and inversely proportional to the internal length scale in a scaled coordinate system.

This study presents a new coupling model (CM) of finite element (FE) and peridynamics (PD), in which only very few PD nodes exist. In the coupling model, PD subregion is directly coupled with FE subregion without an overlapped zone, and the force is transferred between PD nodes and finite elements by a connection stiffness matrix. Since dynamic transformation technique is implemented, PD subregion is adaptively generated and evolved, and ensure that the whole damage process is completed. In addition, as an optimization of the coupling model, a densified-material-point model (DMPM) is achieved, which can remove the limitation of element type and enhance the flexibility of the coupling model. As a result, the computational efficiency of coupling algorithms will be greatly improved, and numerical error can be overcome in inferring the damage region. The capability of the developed coupling model was demonstrated by the stretch examples of plates with different discrete cases, and damage analysis was further conducted to demonstrate the strong capability of the DMPM in capturing failure mode.

Lightweight design has had an important role to play in recent gear developments. One way of reducing gear weight is to apply a shot-peening process in addition to the usual case-hardening because the higher compressive residual stresses within the material mean that the same torque values can be transmitted with smaller gears. However, due to the compressive residual stresses, fisheye failures at non-metallic inclusions can occur, which have an effect on the endurance fatigue strength of high-strength gears, especially in the very high cycle fatigue range. This paper presents a detailed FEM simulation of the stress state at a non-metallic inclusion in the tooth root fillet of such high-strength gears. The aim is to explain certain fracture characteristics, which differ from fisheye failures of standard specimens. With the results of the simulation und taking into consideration the fracture characteristics determined in a SEM, a fracture analysis for fisheye failures in the tooth root fillet of high-strength gears is carried out that links different theories found in the literature. Subsequently, this analysis and the influence of residual stresses are compared with data and further fracture analyses from experimental investigations found in the literature.

Peridynamic (PD) models are commonly implemented by exploiting a particle-based method referred to as standard scheme. Compared to numerical methods based on classical theories (e.g., the finite element method), PD models using the meshfree standard scheme are typically computationally more expensive mainly for two reasons. First, the nonlocal nature of PD requires advanced quadrature schemes. Second, non-uniform discretizations of the standard scheme are inaccurate and thus typically avoided. Hence, very fine uniform discretizations are applied in the whole domain even in cases where a fine resolution is per se required only in a small part of it (e.g., close to discontinuities and interfaces). In the present study, a new framework is devised to enhance the computational performance of PD models substantially. It applies the standard scheme only to localized regions where discontinuities and interfaces emerge, and a less demanding quadrature scheme to the rest of the domain. Moreover, it uses a multi-grid approach with a fine grid spacing only in critical regions. Because these regions are identified dynamically over time, our framework is referred to as multi-adaptive. The performance of the proposed approach is examined by means of two real-world problems, the Kalthoff–Winkler experiment and the bio-degradation of a magnesium-based bone implant screw. It is demonstrated that our novel framework can vastly reduce the computational cost (for given accuracy requirements) compared to a simple application of the standard scheme.

As a significant extension of classical structures, elastic wave metamaterials are widely applied to the vibration isolation and turning wave propagation. However, little attention has been paid on their fracture and arrest properties. In this work, the dispersion curves and arrest property of mode II crack in 2D elastic wave metamaterials are studied, in which both nonlocal interactions and local resonators are considered. Because every unit cell is connected to the second nearest neighboring one with the massless spring along the x-direction, the nonlocal interaction is achieved. The dynamic effective mass is derived and influences of nonlocal interactions on the dispersion relation are analyzed. Moreover, the energy release ratio which characterizes the arrest ability is derived and the effects of structural parameters are discussed. The theoretical predictions are also compared to the finite element simulation. Numerical results show that the crack propagation resistance of mode II crack can be improved significantly by introducing proper nonlocal springs within a finite steady-state region. But in the oscillation region, the energy release ratio G0/G is unstable. Furthermore, an additional energy barrier can be generated before the region in which the crack propagates stably.

In a recent contribution, Shrimali and Lopez-Pamies (Extreme Mech Lett 58, 101944, 2023a) have shown that the Griffith criticality condition that governs crack growth in viscoelastic elastomers can be reduced—from its ordinary form involving a historically elusive loading-history-dependent critical tearing energy \(T_c\)—to a fundamental form that involves exclusively the intrinsic fracture energy \(G_c\) of the elastomer. The purpose of this paper is to make use of this fundamental form to explain one of the most telltale fracture tests for viscoelastic elastomers, the so-called delayed fracture test.