A failure criterion for brittle elastic materials under mixed-mode loading

The failure criterion of Leguillon at reentrant corners in brittle elastic materials (Leguillon 2002, Eur J Mech A/Solids 21: 61–72; Leguillon et al. (2003), Eur J Mech A—Solids 22(4): 509–524) validated in (Yosibash et al. 2004, Int J Fract 125(3–4): 307–333) for mode I loading is being extended to mixed mode loading and is being validated by experimental observations. We present an explicit derivation of all quantities involved in the computation of the failure criterion. The failure criterion is validated by predicting the critical load and crack initiation angle of specimens under mixed mode loading and comparison to experimental observations on PMMA (polymer) and Macor (ceramic) V-notched specimens.     

The elliptic paraboloid failure criterion for cellular solids and brittle foams

Summary Cellular solids and brittle foams are increasingly finding application in constructions mainly as core materials for loaded sandwich structures where the loading of the structure generates multiaxial stress states on them. It has been established that the principal mechanism of deformation is based on the cell-wall bending and closed-cell as well as open-cell foams present similar stiffnesses. Therefore simple relations are found for their tensile, compressive and shear strengths and their elastic properties.It has been established in this paper that the modes of failure of such materials can be satisfactorily described by the elliptic paraboloid failure criterion for the general orthotropic body. Then, as soon as the yield or failure stresses in simple tension and compression are measured along the three principal stress directions of the material the failure locus is unequivocally defined and all the properties of the material under any complicated load can be accurately established. However, since these materials fail in the compression-compression-compression octant of the principal stress space by elastic buckling, the EPFS-criterion is cut-off by an ellipsoid surface, with intercepts along the principal axes the respective compressive failure stresses.The criterion thus established yields satisfactory results. It has been tested among others in a reticulated vitreous carbon foam as well as in an aluminium foam. The experimental results for these foams existing in the literature are fitting better with this universal criterion than any other considered, thus indicating the validity of the elliptic paraboloid failure criterion also for this type of materials.     

Crack-growth criterion for dynamic brittle fracture

An approach to the solution of problems of the mechanics of brittle dynamic fracture, which is based on the energy principle and the principle of time separation, is proposed. A so-called wave criterion of fracture, which can be used to estimate dynamic crack growth in an elastic body, is formulated on the basis of these principles. A general procedure is described for this estimation, and a comparison is made between experimental and theoretical values of crack-growth rate in a rectangular bar in a plane stress state (PSS); this confirms the applicability of the developed approach for engineering calculations.Translated from Problemy Prochnosti, No. 2, pp. 12–18, February, 1994.     

A failure criterion for brittle and quasi-brittle materials under any level of stress concentration

In this paper, we present a new criterion to predict the crack initiation under quasi-static loads from a geometrical weakness presenting an arbitrary stress concentration in brittle or quasi-brittle materials. Three material parameters were used in the establishment of the criterion, namely the ultimate stress σ_c, the critical energy release rate for crack growth G_c and the critical energy release rate for fracture under uniform uniaxial tension G_u. The use of these two critical energy release rates was justified by the observation of the fracture surfaces under different stress concentrations. The proposed three parameters’ concept enables to take the different stress concentration levels into account, thus provides a unified criterion to predict crack initiation for any stress concentration, whatever it is singular or regular. Numerous experimental studies were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed criterion is physically reasonable, highly accurate and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle or quasi-brittle materials.     

A statistical strength criterion for brittle materials

Based on a probabilistic model of brittle microfracture (microdamage) leading to macrofracture of materials, we propose a statistical interpretation of strength criteria, which relate start of macrofracture (manifested by macrocrack formation in tension or internal structure stability loss in compression) with attainment of a certain (critical) value of density of microdefects in the material under study. The criterion is reduced to comparative analysis of microdefect density induced by the particular loading type and its critical value, which is intricnsic to this material and is invariant to the stressed state type.     

Three-parameter yield criterion for a brittle polyester resin

The tensile and compressive strengths of three polyester resins were measured under superposed hydrostatic pressure extending to 300 MPa, in an attempt to establish yield criteria. The polyesters were brittle in uniaxial tension at all pressures, and accordingly, a third testing geometry, diametral compression of a disc, was employed to complete the two or three necessary parameters to establish the yield surface in stress space. From the biaxial (disc) and axial compressive test data, the atmospheric tensile yield strength (higher than the fracture strength) was computed to be ～67 MPa in comparison with the compressive strength of ～120 MPa, their ratio 0.56 being significantly less than the more common 0.75 found for thermoplastics and epoxides. The data for compressive yield strength under superposed pressure were compared with the predictions of the two-parameter pyramidal, conical and paraboloidal criteria and the fit, though reasonable for the latter, could be significantly improved if a further independent material parameter was employed to give a three-parameter pyramidal criterion (the principal stresses σ₁, σ₂ and σ₃ being measured in MPa) of the form 0.0150σ₁?0.0039σ₂?0.0083σ₃=1     

A general mixed-mode brittle fracture criterion for cracked materials

In order to predict the fracture direction and fracture loadings of cracked materials under the general mixed-mode state, this paper presents a new general mixed-mode brittle fracture criterion based on the concept of maximum potential energy release rate (MPERR). This criterion can be easily degraded to the pure-mode fracture criterion, and can also be reduced to the commonly accepted fracture criteria for the mixed-mode I/II state. In order to validate the proposed criterion, we have carried out the experiments with aluminium alloy specimens under various mixed-mode loading conditions. The experimental results agree well with the predictions of the proposed criterion.     

A criterion study for non-singular stress concentrations in brittle or quasi-brittle materials

In engineering applications, it is difficult to avoid the non-singular stress concentrations that often play an important role in structure designs. The simplest engineering strength criteria are in general not appropriate due to their incapacity in dealing with important size effect induced by stress gradients. In this paper, we present first a simple experimentation, which consists of plates with a central hole under uniaxial tensile loading, showing important size effect. Second, numerous criteria, including commonly used engineering criteria, crack initiation criteria based on the finite fracture mechanics, or cohesive criteria, were adapted to fit the experimental results. We found that most of these criteria, including criteria with a single material parameter and those with two material parameters, are not suitable for fracture prediction of materials under non-singular stress concentrations. It seems that three material parameters would be the minimum to establish an adequate fracture criterion for arbitrary stress concentrations. By analysing the energy dissipation of micro-crack bands under different stress concentrations, we proposed a new fracture criterion with three material parameters based on the finite fracture mechanics. It is shown that this criterion can provide accurate critical remote loads comparing with experimental data. We believe that the three parameter concept is physically reasonable and can be used in establishing fracture criteria in both the cases of singular and non-singular stress concentrations.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

A statistical strength criterion for low temperature brittle fracture of metals

A statistical approach is presented to strength analysis of metals under conditions of low-temperature embrittlement. The approach involves two categories of defects leading to fracture: primary defects, present in the original structure in the form of microvoids, microcracks, inclusions etc., and secondary defects, formed under load through the action of the dislocational mechanisms involved in initiation of crack nuclei.An arbitrary pattern of primary and secondary defects is considered, on the assumption of approximate stochastic independence. This permits determination of the probability of brittle fracture under any mode of stressing. Development of a major crack is treated as a multistage process, whereby fracture may be considered either as a sequence of violated limit equilibria, or as a discontinuous Markov process. The role of thermal fluctuations in the latter case is demonstrated. As an example, limiting fracture-stress curves are determined for a plane model based on Stroh's mechanism. Results show that the temperature dependence of the fracture stress is governed by the mode of stressing and by the structure of the material.     

Adiabatic shear failure in brittle solids

Recent studies have revealed microscopic amorphous lamella resulting from inelastic deformation in the ballistic impact of boron carbide ceramic. The possibility that these deformation features are a consequence of adiabatic shear deformation in the impact event is explored. An early theory of adiabatic shear that was limited to the response of rigid-plastic deformation is expanded to include elastic strain energy. The study reveals that elastic strain energy is commonly a small, but not negligible, contribution to impact-induced adiabatic shear in metals. Elastic strain energy is paramount in brittle solids. Relations are developed from the theory to predict the nominal width and spacing of adiabatic shear-bands in brittle solids. Comparisons of the theoretical predictions are consistent with observations of impact-induced deformation features in boron carbide.     

An energy criterion for fatigue failure

A criterion for the fatigue failure of metals is presented which is based on specific energy dissipation during the loading cycle. Equations are obtained which determine the relative critical failure energy for cyclically unstable materials. The parameters used were studied as functions of the mean stresses. An experimental study of the criteria was carried out using regular and programmed loading on cyclically softening steels 45 and 12KhN3A in the as-received condition.Translated from Problemy Prochnosti, No. 1, pp. 3–10, January, 1993.     

Microscopic-damage-based criterion for fatigue failure prediction

A computer-aided X-ray rocking curve analyser was developed to monitor the accrued microstructural damage occurring during low cycle fatigue of an aluminium alloy. These results indicated a linear relationship between the X-ray rocking curve half-width and the fraction of life. The resultant damage-assessment curve provided a nondestructive means of estimating the time to failure in a sample with unknown prior loading history. This failure criterion was found to be independent of the strain amplitude and was equally applicable to either high cycle or low cycle fatigue.     

Experimental studies on shear failure of freeze-bonds in saline ice: Part I. Set-up, failure mode and freeze-bond strength

The strength of freeze-bonds in thin saline ice has been investigated through two series (in 2008 and 2009) of experiments in the Hamburg Ship Model Basin (HSVA) as a function of the normal confinement (σ), the submersion time (Δt) and the initial ice temperature (T_i). The freeze-bonds were mostly formed in a submerged state, but some were also formed in air. The experimental set-up was improved in the 2009 experiments. In 2008 a ductile-like failure mode dominated (78%), whereas in 2009 the brittle-like dominated (93%). We suggest that this is a combined ice and test set-up effect. The 2009 experimental procedures allowed for careful sample handling giving higher strength and it was softer. Both these things should provoke a more brittle-like force-time response. The average freeze-bond strength in brittle-like samples was around 9 kPa while in ductile-like samples was around 2 kPa. The maximum freeze-bonds strength were measured for short submersion times, from 1 to 20 min, and reached a maximum value of 30 kPa.A Mohr-Coulomb like failure model was found appropriate to represent the freeze-bond shear strength as function of the normal confinement. Saline freeze-bonds in saline water had cohesion/friction angle around 4 and 1.4 kPa/25° for the brittle- and ductile-like samples respectively, which fitted well with previously published data.A bell-shape dependence for τ_c vs. Δt was found, which agreed with the predictions by Shafrova and Høyland (2007). We suggest that this is essentially a freeze-bond porosity effect and propose three phases in time with subsequent cooling, heating and equilibrium to account for this trend. Qualitative experiments showed that the submersion time and the initial ice temperature were strongly coupled.To account for the connection between contact time, block dimensions and ice properties and the freeze-bond strength, dimensionless number were used. Fourier scaling was more appropriate than Froude scaling to scale freeze-bonds.The freeze-bonding made in air developed fast (in less than 30 s) when the ice was cold and dry, but no freeze-bonding occurred for the same contact times when the ice was warm and wet.