Strain Failure Criterion Research Articles

Nonlinear analysis of edge effects in angle-ply laminates

An initial stress iteration method using a quasi-three-dimensional finite element has been developed for the nonlinear analysis of Carbon Fibre Reinforced Plastic (CFRP) laminates subjected to a uniform inplane load. Linear and nonlinear analyses of the free edge problem were carried out for the [0/90] s, and [ ± 45] s laminates with and without resin layers included between plies of laminae. The nonlinear results show that the peak shear stress in the [0/90] s laminate and all the stress components in the [±45], laminates are reduced. A maximum strain failure criterion was used and failure modes were predicted.

Non-linear analysis of tapered (in steps) laminated plate under uniform inplane load

An initial stress iteration method using a quasi-three-dimensional element has been developed for the material non-linear analysis of Carbon Fibre Reinforced Plastic (CFRP) laminates of infinite width subjected to a uniform inplane load. Analyses of variable thickness (stepped) laminated plates with various arrangements for the ply fibre directions have been carried out. Linear and non-linear numerical results are given for a single step plate with resin layers included. The non-linear results show that peak stresses predicted by the linear analysis are reduced. This is a result of non-linear (plastic) deformation of the resin. A maximum strain failure criterion is used and failure modes of the free edge and stepped plate problems are predicted. The delaminating stress for the [90/90/90/90] s stepped plate compares well with experiments.

Response of Quasi-Isotropic Carbon/Epoxy Laminates to Biaxial Stress

The results of biaxial tension tests on AS4/3501-6 carbon/epoxy are presented for a quasi-isotropic [90, ±45,0]s laminate. These tests were performed using a tubular spec imen subjected to internal pressure and axial tension. The specimen design appears to minimize stress concentrations in the gage section. The measured stress-strain response shows a small but definite reduction in stiffness associated with progressive matrix failure. The failure stresses and strains are consistent with a maximum fiber strain failure criterion, and are most accurately modeled with a progressive failure model that incor porates ply stiffness changes.

Fatigue of Composites—Fatigue Modulus Concept and Life Prediction

Fatigue behavior of glass fiber reinforced epoxy composite materials has been studied analytically. A new concept called "fatigue modulus," which is defined as a slope of applied stress and resultant strain at a specific cycle is introduced. Fatigue modulus degradation is studied using an assumption that the fatigue modulus degrada tion rate follows a power function of fatigue cycle. Theoretical equation for predicting fatigue life is formulated using the fatigue modulus and its degradation rate. This rela tion is simplified by strain failure criterion for the practical application. It is proved that the final formula predicts the fatigue life of a glass fiber epoxy composite material better than S-N curve or Basquin's relation. An attempt is made to find the relation ship between fatigue modulus and elastic modulus by the geometric relation from stress-strain curve under the cyclic loading.

Yield and ultimate strengths of fibre composite laminates

A modified maximum strain failure criterion is proposed to predict the failure of the laminae of fibre-reinforced composites when the laminate is subjected to combined loading. The criterion includes two levels of failure. The lower level predicts the onset of stiffness degradation or ‘yield’ in the lamina. Beyond this level the lamina response is non-linear until the upper lever is reached, which corresponds to ‘ultimate’ failure. After the ultimate failure of a ply in a laminate in a certain mode it is assumed that the failed layer unloads gradually in the same mode only. The theoretical predictions of the present analysis are compared with predictions of other failure theories as well as with experimental data obtained from tests on composite tubular specimens.

Stability prediction for the Zinkgruvan Mine, Central Sweden : Borg, T; Leijon, B; Roshoff, K; Stephansson, O Proc ISRM Symposium on Design and Performance of Underground Excavations, Cambridge, 3–6 Sept 1984P113–121. Publ London: British Geotechnical Society, 1984

The geomechanics of the Zinkgruvan Mine are presented. A new approach for performing rock stress measurements in open stopes and drifts was tested. An elastic FEM model and strain failure criteria ...

A Comparative Study of Failure Envelopes in Composite Laminates

On the basis of a recent survey conducted by AIAA composite structures subcom mittee, the failure criteria used by more than ninety percent design engineers have been considered in this study. These failure criteria are maximum stress, maximum strain and quadratic polynomial (Tsai Wu, Chamis, Hoffman and Hill) failure criteria. Failure envelopes for all these failure criteria are drawn for (0/90/±45)s laminate made of T300/5208 graphite epoxy material in stress space. For the first ply failure strength, we observe a great deal of difference in the predictions made by these failure criteria. Depending upon the failure criteria being compared, the maximum percentage dif ference ranges to 75%. Because of the criticality of failure criteria in structural design, for a better confidence in the predicted strength, it is necessary to undertake further theoretical and experimental studies in failure criteria. Computer aided optimum designs may not be optimum if the correct failure criteria is not considered.

A unifying strain criterion for fracture of fibrous composite laminates

A general fracture toughness parameter Q c which is independent of layup, was previously derived using a strain failure criterion for fibers in the principal load-carrying plies. It was verified to be a material constant for centrally cracked boron/aluminum composite specimens. The specimens were made with various proportions of 0° and ±45° plies. Moreover, a limited amount of data indicated that the ratio Q c/ϵ tuf , where ϵ tuf is the ultimate tensile strain of the fibers, might be a constant for all composite laminates, regardless of material and layup. In that case, a single value of Q c/ϵ tuf could be used to predict the fracture toughness of all fibrous composite laminates from only the elastic constants and ϵ tuf . To verify that Q c/ϵ tuf is indeed a constant, values of Q c/ϵ tuf are calculated and presented here for centrally cracked specimens made from graphite/polyimide, graphite/epoxy, E-glass/epoxy, boron/epoxy. and S-glass-graphite/epoxy materials with numerous [0 i/±45 j/90 k] layups. The data indicate that Q c/ϵ tuf is reasonably constant for all laminates that did not delaminate or split extensively in the 0° plies at the crack tips. But some elevation of Q c/ϵ tuf due to small-to-moderate crack-tip damage is evident. Using a single value of Q c/ϵ tuf for all the layups and materials, strengths were predicted for the test specimens. The predicted and test values agree well except, of course, for the laminates that delaminated or split extensively. Then, the predicted strengths are usually conservative. Layup affects the ratio of cracked to uncracked strengths more for the resin matrix specimens than the boron/aluminum specimens.

Angled Elliptic Notch Problem Under Biaxial Loading

The strain failure criterion proposed by the second author is applied to obtain general solutions for the angled elliptic notch problem subject to uniform biaxial loading. The solutions can be reduced to those for uniaxial tension, uniaxial compression, or pure shear as special cases. The solution for the case of pure shear is compared with experimental data found in literature. It is remarked that the present theory involves material parameters and predicts that fracture behavior is dependent on materials being investigated.

STRUCTURAL FAILURE IN SELECTED RAW FRUITS AND VEGETABLES1

ABSTRACTA torsion test was developed for studying the structural failure of selected raw fruits and vegetables. Apple, melon and raw potato flesh were tested at a shear strain rate of approximately 0.26s‐1 in torsion and uniaxial compression. Low strain modulus values were determined in addition to shear stresses and normal strains at failure.Results corroborated the maximum normal strain failure criterion proposed by Segerlind and Dal Fabbro (1978) for apples and suggested its application to potatoes and melons if true strains are used rather than engineering strains. The maximum shear stress theory also seemed to be a possible failure criterion for potatoes. Results comparing compressible and incompressible materials suggest that bulk strain affects the shear stress at failure. The observed failure planes supported the quantitative results for stresses at failure. Scanning electron micrographs indicated that the cellular failure occurred in the cell wall, regardless of whether it was due to tension,Varying specimen lengths or diameters had negligible effects on the uniaxial compression modulus but did affect the shear stress at failure in a manner yet to be satisfactorily explained.

Angled Elliptic Notch Problem in Compression and Tension

The strain failure criterion previously proposed by the first author is applied to obtain solutions for the angled elliptic notch problem subject to compressive and tensile loads. The theory compares favorably with experiments in both cases. This indicates that the proposal of the crack plane being normal to the direction of the maximum tensile strain for brittle fracture is essentially correct.

Optimal Design of Anisotropic (Fiber-Reinforced) Flywheels

An analysis is given of the kinetic energy storage capacity of anisotropic flywheels. Using a uniform strain failure criteria, the optimal shapes of flywheels are determined as a function of the degree of anisotropy. Within this spectrum of shapes, practical design considerations are shown to favor the case where there is equal reinforcement in the radial and circumferen tial directions. Comparisons are made between the present solid-wheel-type design and the ring design.

Crack initiation in plain concrete

Synopsis At the tip of a sharp crack or re-entrant notch, the stresses calculated by a simple elastic analysis become infinite. Consequently, maximum-stress or -strain failure criteria and stress-concentration factors cannot be used to predict failure at such points. The linear elastic fracture mechanics theory can, however, be applied. In the paper, a brief treatment of the application of this theory to sharp cracks in concrete beams is presented and the effect of beam size is particularly examined. The same basic technique is applied to re-entrant notches. Experimental evidence of the validity of the approach is given. Theoretical results are included which allow these test data to be extended to a wide range of notch conjigurations. It is expected that this work will have considerable importance for the problem of crack initiation at corners of openings in walls etc.

A micromechanical analysis of crack propagation in an elastoplastic composite material

The mathematical theory of plasticity, incorporating the Prandtl-Reuss flow rule and an octahedral shear stress-plastic octahedral shear strain yield and failure criterion, has been combined with a finite element numerical analysis to model the initiation and subsequent propagation of a crack in a filament-reinforced composite material. An applied loading transverse to the unidirectional reinforcement is assumed, the goal being to develop a better understanding of the failure mechanisms influencing off-axis strength, in terms of the governing micromechanical parameters.

Structural integrity of an ablating rocket subjected to axial acceleration

One of the important design conditions for solid propellant rocket motors is that of inertia loading due to long term storage at 1 g, or acceleration in short time to high g. This paper investigates the structural integrity for inertia loading of a long, bonded, thick-walled cylinder, and includes the parametric considerations of rocket diameter 26, web fraction X, inertia g-level n, and reduced burnout time t//ar, as well as employing typical propellant properties and allowing for various burning rates of the eroding boundary. Finite end effect correction factors can be included from references already in the literature. By assuming a maximum shear strain failure criterion, a design envelope is obtained of pgnob vs t//ar, which expresses the interaction among the various parameters.

On the resistance of ductile materials to combined stresses in two or three directions perpendicular to one another

An analysis of distortional, i.e. constant volume, bulk material failure of incompressible hyperelastic elastomers in multiaxial loading conditions is presented. The present work describes deformation-based failure surfaces in terms of strain and stretch because stress-based descriptions render impractical. Classical as well as generalized strain and stretch-based failure criteria are reviewed regarding their suitability for hyperelastic polymers in their entropy-elastic regime. Classical criteria, such as the normal strain hypothesis or a von Mises-like strain criterion, prove inadequate for hyperelastic elastomers. Instead, the present work proposes a strain-based formulation of the generalized Podgórski–Bigoni–Piccolroaz criterion. This reformulation allows for an accurate description of failure surfaces of natural and synthetic rubber, filled and unfilled vulcanizates as well as silicones. It describes the failure surface in a single equation and can be readily implemented in finite element codes. For parameter identification, standard tests of soft polymers such as bulge test, uniaxial tension or planar tension test can be used.