196,063 research outputs found
Universal equations for the mode I stress distribution in finite size orthotropic plates with blunt notches and holes
No full textIn this work a new universal formula suitable for accurately describing the maximum normal stress distribution along the entire ligament of orthotropic plates weakened by central holes or symmetric lateral notches is provided. To this end, a recent analytical solution proposed to describe the local stress distributions in the close neighbourhood of U- and V-shaped notches is significantly improved using an asymptotic matching approach which explicitly introduces in the analytical formulation two new parameters able to account for the global size of the notched component. The comparison with a large bulk of numerical results reveals that the new solution proposed is very accurate for many geometrical variations, from lateral notches and central holes. Accordingly, it represents a useful engineering tool to calculate the normal stress field ahead of several geometrical variations in orthotropic plates under tension
Strain fields in cracked bodies under antiplane shear for a generalised non-hardening material law
No full textAn exact, closed form, solution is derived for the non-linear stress distribution in a cracked body under antiplane shear deformation. A generalised, non work-hardening, law is introduced to describe the material behaviour, and the stress and strain fields are derived in closed form. Such a new generalised material law includes the effect of a new parameter, a, which allows the transition from the ideally elastic behaviour (low strain regime) to the pure non-linear behaviour (large strain regime) to be modulated. A discussion is carried out on the features of the new solution and on the behaviour of stresses and strains close to and far away from the crack tip
Mode I Generalised Stress Intensity Factors for rounded notches in orthotropic plates
No full textIn this paper, taking advantage of a recent analytical solution for the stress fields in notched orthotropic plates under tension, new equations are provided for the mode I Generalised Stress Intensity Factor (GSIF) in the case of rounded notches. Such equations explicitly consider the role played by the material properties and the notch opening angle, and inherently quantify the stress redistribution due to the finite value of the root radius with respect to the pointed notch case. The main features of the GSIFs when applied to rounded notches are discussed, as well as the combined effect of the notch root radius and the elastic properties of the material.
The developed new equations are then used to provide an engineering formula to assess the stress concentration factor of orthotropic plates with notches.
Eventually, a GSIF-based fracture criterion is proposed for notched orthotropic plates under mode I, and its validity is discussed against some experimental data on notched composite laminates taken from the literature
Static notch sensitivity in orthotropic materials and composites
No full textA theoretical study on defect and notch sensitivity in orthotropic materials is carried out, with the aim to make explicit the bridging between notch effect and defect sensitivity. Analogies and differences with the isotropic case are highlighted, and the relevant parameters necessary to quantify the transition from a fracture-mechanics-controlled to a notch-mechanics-controlled behaviour are discussed in details. The validity of the proposed approach is proven taking advantage of a bulk of experimental data taken from the literature and related to thermoplastic and thermosetting composite laminates with different stacking sequences and notch geometries
Understanding the effect of notches in orthotropic solids subjected to static loads
No full textThe main aim of the present paper is to propose and validate a new and simple diagram able to explain the effect of geometrical variations in orthotropic solids under static loads. The derived approach accounts for the effect of the local geometry of the notch as well as for the relevant material properties and highlights the parameters drawing the demarcation line from notch insensitivity, incomplete notch sensitivity and full notch sensitivity. In particular, it is demonstrated that when the notch depth is smaller than a characteristic length, aF, the notch does not have a detrimental effect and the design of the mechanical part can be carried out disregarding the geometrical variation. Differently, when the notch depth is larger than aF, full notch sensitivity or incomplete notch sensitivity can occur, depending on the actual value of the notch root radius. The soundness of the proposed diagram is checked against experimental data previously published in the literature and related to short fibre reinforced composites
Effect of material orthotropy on the notch stress intensity factors of sharp V-notched plates under tension
No full textIn this paper, an analytical and numerical study is carried out on the role played by the elastic properties of orthotropic materials on the Notch Stress Intensity Factors (NSIFs) of pointed V-notches on plates under tension. In the first part of the work, new analytical solutions are presented to approximate the NSIFs of shallow and deep symmetric notches in Double Edge Notched plates under Tension (DENT). Subsequently, a comprehensive numerical study is carried out on finite size notches considering different orthotropic materials, with the aim to make explicit the effect of material orthotropy on the NSIFs. Eventually, based on a best fitting procedure of the numerical results, accurate expressions for the NSIFs are provided, and their degree of accuracy is discussed against data from the literature and results from ad hoc numerical analyses
Antiplane shear stresses in orthotropic plates with lateral blunt notches
No full textThis contribution investigates the stress fields in orthotropic plates featuring lateral notches under anti-plane shear loading. Four different notch geometries are considered and the relevant analytical expressions for the stress distribution are derived in closed form. For each geometry, the main features of the stress fields and the accuracy of the analytical expressions developed are discussed comparing theoretical results and numerical data from FE analyses carried out on finite plates under longitudinal shear
Three-dimensional stress fields due to notches in plates under linear elastic and elastic-plastic conditions
No full textThe paper deals with a 3D multi-parametric stress field representation ahead of notches in plates of finite thickness under different loading conditions. Under certain hypotheses, the 3D governing equations of elasticity can be reduced to a system where a bi-harmonic equation and a harmonic equation have to be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, and the latter provides the solution of the corresponding out-of-plane shear notch problem. The solution is valid close the notch edge, through the plate thickness, with exclusion of a very limited zone close to the free surface of the plates. Also, under elastic-plastic conditions there are circumstances where it is possible to separate the in-plane problem from the out-of-plane problem. A new analytical frame is proposed, and the results are compared with those obtained from 3D finite element models of a plate with a square notch. In the presence of remote applied tensile stress, the slope of the induced, out-of-plane, shear stress component matches that of the mode III plastic problem
Bodies described by non-monotonic strain-stress constitutive equations containing a crack subject to anti-plane shear stress
No full textIn this paper the state of stress and strain close to sharp cracks in bodies subjected to an anti-plane state of stress is studied within the context of a non-monotonic strain-stress relation within the context of a generalization of the Cauchy theory of elasticity, providing an exact analytical solution to the problem. A discussion is provided to highlight the main features of stress and strain distributions, and the implications of the new theory for fracture assessments. In particular, it is proved that the intensity of the complete stress field can be expressed as a function of the Stress Intensity Factor K III , as in the case of conventional linearized elasticity theory, thus promoting a K based-approach to the fracture of elastic solids obeying a constitutive relation wherein the linearized strain is expressed as a non-linear function of the Cauchy stres
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