Showing papers in "International Journal of Fracture in 2022"

Fatigue fracture morphology of AISI H13 steel obtained by additive manufacturing

Abstract: Abstract The paper focuses on researching the effect of fatigue loading on metallic structure, lifetime, and fracture surface topographies in AISI H13 steel specimens obtained by selective laser melting (SLM). The topography of the fracture surfaces was measured over their entire area, according to the entire total area method, with an optical three-dimensional surface measurement system. The fatigue results of the SLM 3D printed steel specimens were compared with those reported for conventionally manufactured 13H steel. The investigation also considers the roughness of the specimens’ side surface. Moreover, the fractographic evaluation conducted using scanning electron microscopy confirms that the predominant fracture mechanism is transgranular fracture. Microtomography done after mechanical loading also showed the influence of the stress level on the porosity distribution. Both fractographic and Micro-CT investigations confirm that higher stresses result in coarser and much more uniform porosity observed in fractured samples. These comprehensive quantitative and qualitative fracture analyses are beneficial to predict the failure conditions of SLM steel parts, especially in the case of fatigue damage. From the quantitative analysis of the H13 SLM-manufactured fracture surface topography, it was possible to conclude that the larger the loadings acting on the specimen, the rougher the fracture surface because the ductile fracture mode dominates. It has also been proven that the porosity degree changes along the length of the sample for the most stressed specimens.

An efficient implementation of a phase field model for fatigue crack growth

Abstract: Abstract Recently, phase field modeling of fatigue fracture has gained a lot of attention from many researches and studies, since the fatigue damage of structures is a crucial issue in mechanical design. Differing from traditional phase field fracture models, our approach considers not only the elastic strain energy and crack surface energy, additionally, we introduce a fatigue energy contribution into the regularized energy density function caused by cyclic load. Comparing to other type of fracture phenomenon, fatigue damage occurs only after a large number of load cycles. It requires a large computing effort in a computer simulation. Furthermore, the choice of the cycle number increment is usually determined by a compromise between simulation time and accuracy. In this work, we propose an efficient phase field method for cyclic fatigue propagation that only requires moderate computational cost without sacrificing accuracy. We divide the entire fatigue fracture simulation into three stages and apply different cycle number increments in each damage stage. The basic concept of the algorithm is to associate the cycle number increment with the damage increment of each simulation iteration. Numerical examples show that our method can effectively predict the phenomenon of fatigue crack growth and reproduce fracture patterns.

Uncertainty quantification in fatigue crack-growth predictions

Abstract: Abstract The reliability of the damage tolerance approach to engineering design is affected by numerous sources of uncertainty that can lead to unsafe predictions, in turn jeopardizing the safety of structures. This work presents a robust stochastic framework for fatigue crack-growth predictions applied to a round bar under tension–compression loading conditions. Multi-source uncertainties were taken into account to derive the lifespan distribution for the bar in such a way to cover the uncertainties typically appearing in a structural integrity assessment. The sensitivity of each input variable was obtained and the influences of variables on the life predictions were derived and ranked accordingly.

A multi-resolution approach to hydraulic fracture simulation

Abstract: Abstract We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

Energetically motivated crack orientation vector for phase-field fracture with a directional split

Abstract: Abstract The realistic approximation of structural behavior in a post fracture state by the phase-field method requires information about the spatial orientation of the crack surface at the material point level. For the directional phase-field split, this orientation is specified by the crack orientation vector, that is defined perpendicular to the crack surface. An alternative approach to the determination of the orientation based on standard fracture mechanical arguments, i.e. in alignment with the direction of the largest principle tensile strain or stress, is investigated by considering the amount of dissipated strain energy density during crack evolution. In contrast to the application of gradient methods, the analytical approach enables the determination of all local maxima of strain energy density dissipation and, in consequence, the identification of the global maximum, that is assumed to govern the orientation of an evolving crack. Furthermore, the evaluation of the local maxima provides a novel aspect in the discussion of the phenomenon of crack branching. As the directional split differentiates into crack driving contributions of tension and shear stresses on the crack surface, a consistent relation to Mode I and Mode II fracture is available and a mode dependent fracture toughness can be considered. Consequently, the realistic simulation of rock-like fracture is demonstrated. In addition, a numerical investigation of $$\Gamma $$ Γ -convergence for an AT-2 type crack surface density is presented in a two-dimensional setup. For the directional split, also the issues internal locking as well as lateral phase-field evolution are addressed.

Fatigue behaviour of laser powder bed fusion (L-PBF) Ti–6Al–4V, Al–Si–Mg and stainless steels: a brief overview

Abstract: Abstract Fatigue and crack growth characteristics are essential cyclic properties of additively manufactured (AM) components for load-bearing applications, which are less reported in the literature than static properties. The fatigue behaviour of AM components is more complicated than those produced by conventional fabrication techniques (casting and forging) because of the multiplicity of different influencing factors like defect distribution, inhomogeneity of the microstructure and consequent anisotropy. Therefore, it is crucial to understand fatigue performance under different loading conditions to enhance AM application in aerospace, automotive, and other industries. The present work summarises the published literature for fatigue properties of popular metals (Ti–6Al–4V, Al–Si–Mg and stainless steels) produced by the laser powder-bed-fusion (L-PBF) process. Moreover, process parameters, post-processing treatments and microstructures of these alloys are discussed to evaluate the current state-of-the-art of fatigue and crack growth properties of L-PBF metals. The static properties of these alloys are also included to incorporate only those cases for which fatigue behaviour are discussed later in this review to make a correlation between the static and fatigue properties for these alloys. The effects of build orientation, microstructure, heat treatment, surface roughness and defects on fatigue strength and fatigue crack growth threshold are observed and critically analysed based on available literature. This study also highlights the common and contrary findings in the literature associated with various influential factors to comprehensively understand the cyclic loading behaviour of L-PBF produced metal alloys.

A simplified modelling of hydraulic fractures in elasto-plastic materials

Abstract: In this paper the problem of a plane strain hydraulic fracture propagating in an elasto-plastic material is analyzed. A new stress redistribution model for the proximity of the fracture tip is formulated and a resulting plasticity-dependent crack propagation condition is introduced. A modified variant of the KGD problem that accounts for the plastic deformations in the near-tip zone only is proposed. It is demonstrated that this model can be a credible substitute for the full elasto-plastic hydraulic fracture problem in the case of moderate plastic deformation. The crack-tip shielding effect introduced by the plastic deformation is quantified.

Mode II fracture characterization of toughened epoxy resin composites

Abstract: Abstract Epoxy resin used commonly as a matrix for polymer composite materials has good handling properties, but is too brittle. That is why various modifiers are used to increase the flexibility of products based on epoxy resin. This leads to two issues: how to efficiently increase the toughness of the resin without impacting significantly other properties, as well as how to measure the toughness in composite materials. The work aimed to show how the addition of a reactive rubber modifier will affect the fracture toughness of the obtained laminates during the longitudinal shear test (Mode II fracture). In total, three epoxy-glass laminates with different matrices were made and subjected to the End-Notched Flexure test according to ASTM D7905/D7905M standard: (1) the basic matrix of Epidian 6 resin, (2) Epidian 6 modified with the addition of 10% of Albipox 1000 reactive liquid rubber and (3) Epidian 6 modified with the addition of 10% of Hypro 1300X16 ATBN reactive liquid rubber. Based on the obtained results, it can be seen that the modulus of elasticity for the modified laminates was decreased compared to the laminate of pure epoxy resin (by ~ 25%). However, the addition of reactive rubbers increased the fracture toughness of the modified epoxy-glass laminates in the Mode II longitudinal shear test ( G IIc ) by ~ 40–60%. Thus the benefits of modification outweigh the drawbacks if fracture toughness is an important designing consideration in a given application. The applicability of ENF method is successfully tested, but potential drawbacks are indicated—careful control of specimen thickness is necessary.

Scale effects in the post-cracking behaviour of fibre-reinforced concrete beams

Abstract: Abstract The scale effects on the global structural response of fibre-reinforced concrete (FRC) beams subjected to bending are discussed in the framework of Fracture Mechanics by means of the Updated Bridged Crack Model (UBCM). This model predicts different post-cracking regimes depending on two dimensionless numbers: the reinforcement brittleness number , N P , which is related to the fibre volume fraction, V f ; and the pull-out brittleness number , N w , which is related to the fibre embedment length, w c . Both these dimensionless numbers depend on the beam depth, h , which, keeping the other variables to be constant, drives a ductile-to-brittle transition in the post-cracking regime of the composite. The critical value of the reinforcement brittleness number, N PC , allows for prediction of the minimum (critical) specimen size, h min , which, analogously to the minimum fibre volume fraction, V f,min , is required to achieve a stable post-cracking response. Numerical simulations are compared to experimental results reported in the scientific literature, in which FRC specimens, characterized by the same fibre volume fraction but different sizes, are tested in bending.

The revisited phase-field approach to brittle fracture: application to indentation and notch problems

Abstract: In a recent contribution, Kumar et al. (J Mech Phys Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic brittle materials under arbitrary quasistatic loading conditions. The theory can be viewed as a natural generalization of the phase-field approximation of the variational theory of brittle fracture of Francfort and Marigo (J Mech Phys Solids 46:1319–1342, 1998) to account for the material strength at large. This is accomplished by the addition of an external driving force—which physically represents the macroscopic manifestation of the presence of inherent microscopic defects in the material—in the equation governing the evolution of the phase field. The main purpose of this paper is to continue providing validation results for the theory by confronting its predictions with direct measurements from three representative types of experimentally common yet technically challenging problems: (i) the indentation of glass plates with flat-ended cylindrical indenters and the three-point bending of (ii) U-notched and (iii) V-notched PMMA beams.

On the loss of symmetry in toughness dominated hydraulic fractures

Abstract: Fracking, or hydraulic fracturing, is a ubiquitous technique for generating fracture networks in rocks for enhanced geothermal systems or hydrocarbon extraction from shales. For decades, models, numerical simulation tools, and practical guidelines have been based on the assumption that this process generates networks of self-similar parallel cracks. Yet, some field and laboratory observations show asymmetric crack growth, and material heterogeneity is routinely attributed for it. Here, we show that simultaneous growth of multiple parallel cracks is impossible and that a single crack typically propagates asymmetrically in toughness dominated hydraulic fracturing, in which viscous dissipation of the fluid is negligible. In other words, loss of symmetry is a fundamental feature of hydraulic fracturing in a toughness dominated regime and not necessary the result of material heterogeneities. Our findings challenge the assumptions of symmetrical growth of hydraulic fractures commonly made in practice, and point to yet another instability other than material heterogeneity.

Effect of heat treatments and loading orientation on the tensile properties and fracture toughness of AlSi7Mg alloy produced by Laser Powder Bed Fusion

Abstract: Abstract The present study investigates the effect of building orientation and heat treatment routes on the mechanical behavior of the AlSi7Mg alloy (A357) produced by Laser Powder Bed Fusion. The microstructure and mechanical behavior of A357 in the as built, T5 (directly aged) and T6 (solution treated, water quenched and aged) conditions were compared. Tensile properties of the material were evaluated along two main directions (parallel and normal to the building platform), whereas fracture toughness was measured with cracks placed in three orthogonal orientations. The results indicate that the anisotropy in mechanical properties is greatly reduced after T6 temper, but the selection of the best condition between the as built, T5 and T6 temper must consider the main loading directions and possible crack growth orientations associated with the specific application.

A three-dimensional non-local lattice bond model for fracturing behavior prediction in brittle solids

Abstract: In this paper, a 3D non-local lattice bond model is proposed to model fracturing behaviors of materials. First, the formulations and detailed derivation for three-dimensional non-local lattice bond models are obtained by comparing the strain energy stored in a discrete lattice with the classical continuum strain energy. Then, the capabilities of three-dimensional non-local lattice bond models are verified using benchmarks. To further assess the performance of the non-local lattice bond model, fracturing behaviors in brittle solids are predicted. Compared with the previous numerical results, the proposed model demonstrates better performances, which are more consistent with the experimental observations.

A theory of viscoelastic crack growth: revisited

Abstract: A theory of viscoelastic crack growth developed nearly five decades ago is generalized to express traction in the so-called fracture process zone or failure zone as a function of the crack opening displacement (COD). In earlier work, except for minor exceptions, traction was specified as a function of location. The new model leads to a nonlinear double integral equation that has to be solved for the COD before crack growth can be predicted. First, a closed-form, accurate approximation is found for a linear elastic body. We then show that this COD may be easily and accurately extended to linear viscoelasticity using a realistic, broad spectrum creep compliance. An analytical relationship connecting the stress intensity factor to crack speed then follows. Consistent with earlier work, it is defined almost entirely by creep compliance. Five different failure zone tractions are employed; their differences are shown to have little effect on crack growth other than through a speed shift factor. The Appendix discusses initiation of growth.

Fatigue fracture characterization by cyclic material forces in viscoelastic solids at small strain

Abstract: Abstract The study at hand introduces a new approach to characterize fatigue crack growth in small strain linear viscoelastic solids by configurational mechanics. In this study, Prony series with n - Maxwell elements are used to describe the viscoelastic behavior. As a starting point in this work, the local balance of energy momentum is derived using the free energy density. Moreover, at cyclic loading, the cyclic free energy substitutes the free energy. Using the cyclic free energy, the balance of cyclic energy momentum is obtained. The newly derived balance law at cyclic loading is appropriate for each cycle. In the finite element framework, nodal material forces and cyclic nodal material forces are obtained using the weak and discretized forms of the balance of energy momentum and cyclic energy momentum, respectively. The crack driving force and the cyclic crack driving force are determined by the nodal material forces and the cyclic nodal material forces, respectively. Finally, numerical examples are shown to illustrate path-independence of the domain integrals using material forces and cyclic material forces. The existence of the balance of energy momentum and cyclic energy momentum are also illustrated by numerical examples.

Finite Fracture Mechanics extension to dynamic loading scenarios

Abstract: Abstract The coupled criterion of Finite Fracture Mechanics (FFM) has already been successfully applied to assess the brittle failure initiation in cracked and notched structures subjected to quasi-static loading conditions. The FFM originality lies in addressing failure onset through the simultaneous fulfilment of a stress requirement and the energy balance, both computed over a finite distance ahead of the stress raiser. Accordingly, this length results to be a structural parameter, thus able to interact with the geometry under investigation. This work aims at extending the FFM failure criterion to dynamic loadings. To this end, the general requisites of a proper dynamic failure criterion are first shortlisted. The novel Dynamic extension of FFM (DFFM) is then put forward assuming the existence of a material time interval that is related to the coalescence period of microcracks upon macroscopic failure. On this basis, the DFFM model is investigated in case a one-to-one relation between the external solicitation and both the dynamic stress field and energy release rate holds true. Under such a condition, the DFFM is also validated against suitable experimental data on rock materials from the literature and proven to properly catch the increase of the failure load as the loading rate rises, thus proving to be a novel technique suitable for modelling the rate dependence of failure initiation in brittle and quasi-brittle materials.

The effect of constituent particles on the tear resistance of three 6000-series aluminium alloys

Abstract: Abstract This paper investigates the tear resistance of three cast and homogenized 6000-series alloys, namely AA6061, AA6063 and AA6110, all in temper T6, by means of Kahn tear tests. Of each alloy one commercial version and one tailor-made version were studied. The tailor-made alloys were designed to have approximately three times higher content of constituent particles by increasing the amount of Fe and Si in the chemical composition. The aim was to study in what way a higher constituent-particle content affects the tear resistance and properties of the alloys. The research showed that the unit initiation and propagation energies measured from the Kahn tear tests are markedly reduced when the constituent-particle content is increased, and that the tear resistance is reduced by a higher fraction than the failure strain of the smooth tensile tests. No major differences in the fracture mode and the fracture mechanisms between the alloys with normal and with high constituent-particle content were revealed by the use of computed tomography scanning or scanning electron microscopy imaging. It was concluded for the alloys studied that the increased content of constituent particles had a significant effect on the tear resistance, while the fracture mode and mechanisms remained the same.