Probability distribution of fracture elongation, strength and toughness of notched rectangular blocks with lognormal Young's modulus

Dimas, Leon S.; Veneziano, Daniele; Giesa, Tristan; Buehler, Markus J.

doi:10.1016/j.jmps.2015.06.016

Cited by 12 publications

(3 citation statements)

References 32 publications

(47 reference statements)

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“…Of course, variability in bonding properties might also be attributed to inherent surface defects in pregreg due to the fabrication process. Several studies have focused on the overall mechanical response of materials ( Dimas et al, 2016( Dimas et al, , 2015( Dimas et al, , 2014 or interface ( Taleb Ali et al, 2018;Xu et al, 2014;Motamedi et al, 2013;Khokhar et al, 2009Khokhar et al, , 2013Jumel, 2017 ) subjected to propertys heterogeneity induced by cracks, defects, or other types of flaws, and it was found that the material or bonding strengths are sensitive to randomly distributed properties.…”

Section: Introductionmentioning

confidence: 99%

How variability in interfacial properties results in tougher bonded composite joints by triggering bridging

Tao

Alfano

et al. 2020

International Journal of Solids and Structures

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Section: Introductionmentioning

confidence: 99%

How variability in interfacial properties results in tougher bonded composite joints by triggering bridging

Tao

Alfano

et al. 2020

International Journal of Solids and Structures

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“…There is a rich literature regarding crack propagation in multi-phase media, part of which has been driven by the desire to achieve better failure performances. Elastically-heterogeneous materials have been subjected to extensive investigations, including elastostatic analyses of a crack at a bi-material interface [9,10,23,38,45,63], models of elastic solids with smooth Young's modulus distributions [28,29,41], as well as approaches for the design of bio-inspired or 3D-printed composites with enhanced overall toughness [35,51,62]. Recent numerical and experimental studies [39,40] showed that two are the mechanisms responsible for the overall toughening of elastically-contrasted layered media: stress fluctuations induced by the elastic mismatch and crack renucleation at compliant-to-stiff interfaces.…”

Section: Introductionmentioning

confidence: 99%

Effects of plasticity on the anisotropy of the effective fracture toughness

Brach

2020

Preprint

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This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the crack propagates throughout the material and the evolution of the effective toughness as a function of the layer angle. We first study three idealized situations, where only one property among fracture toughness, Young's modulus and yield strength is heterogeneous whereas the others are uniform. We observe that in the case of toughness and strength heterogeneity, the material exhibits anomalous isotropy: the effective toughness is equal to the largest of the point-wise values for any layer angle except when the layers are parallel to the macroscopic direction of propagation. As the layer angle decreases, the crack propagates along the brittle-to-tough interfaces, whereas it goes straight when the layers have different yield strength but uniform toughness. We find that smooth deflections in the crack path do not induce any overall toughening and that the effective toughness is not proportional to either the cumulated fracture energy or the cumulated plastic work. In the case of elastic heterogeneity, the material is anisotropic in the sense of the effective toughness, as the latter varies as a function of the layer angle. Four toughening mechanisms are active: stress fluctuations, crack renucleation, plastic dissipation and plastic blunting. Finally, we consider a layered medium comprised of compliant-tough-weak and stiff-brittle-strong phases, as it is the case for many structural composites. We observe a transition from an interface-dominated to a plasticity-dominated failure regime, as the phase constituents become more ductile. The material is anisotropic in the sense of the effective toughness.

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“…Similar approaches have been taken in studies of weakly heterogeneous composites where the differences between the constituent properties are small. Such methods have been utilized to study the bulk modulus of weakly heterogeneous random composites (Molyneux, J and Beran, M, 1965), evaluate the effective thermal conductivity of polycrystals using weak contrast expansions (Avellaneda and Bruno, 1990), and provide solutions for the effective stiffness and toughness of biomimetic random composites (Dimas et al, 2015a(Dimas et al, , 2015b. Similar approaches have been proposed to evaluate the effective nonlinear properties of composites (Castañeda, 1991).…”

Section: Introductionmentioning

confidence: 99%

Spectral analysis of inhomogeneities shows that the elastic stiffness of random composites decreases with increasing heterogeneity

Ban

2019

Mechanics of Materials

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Investigation of inhomogeneities has wide applications in different areas of mechanics including the study of composite materials. Here, we analytically study an arbitrarily-shaped isotropic inhomogeneity embedded in a finite-sized heterogeneous medium. By modal decomposition of the influence of the inhomogeneity on the deformation of the composite, an exact relation is presented that determines the variation of effective elastic stiffness caused by the presence of the inhomogeneity. This relation indicates that the effective elastic stiffness of a composite is always a concave function of the elastic modulus of the inhomogeneity, embedded inside the composite.Therefore, as the heterogeneity of elastic random composites increases, the rate of increase in effective stiffness caused by the stiffer constituents is smaller than the rate of its decrease due to the softer constitutions. So, weakly heterogeneous random composites become softer and less conductive with increasing heterogeneity at the same mean of constituent properties. We numerically evaluated the effective properties of about ten thousand composites to empirically support these results, characterize the nonaffinity of the displacement field in random composites, characterize the sample to sample variability of the effective properties and extend the results to the thermal conductivity of composites.

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Probability distribution of fracture elongation, strength and toughness of notched rectangular blocks with lognormal Young's modulus

Cited by 12 publications

References 32 publications

How variability in interfacial properties results in tougher bonded composite joints by triggering bridging

How variability in interfacial properties results in tougher bonded composite joints by triggering bridging

Effects of plasticity on the anisotropy of the effective fracture toughness

Spectral analysis of inhomogeneities shows that the elastic stiffness of random composites decreases with increasing heterogeneity

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