Elasticity mechanics - linear-elastic

Fracture Mechanics. Linear elastic fracture mechanics (qv) (LEFM) can be appHed only to the propagation and fracture stages of fatigue failure. LEFM is based on a definition of the stress close to a crack tip in terms of a stress intensification factor K, for which the simplest general relationship is... 

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

The ratio of stress to strain in the initial linear portion of the stress—strain curve indicates the abiUty of a material to resist deformation and return to its original form. This modulus of elasticity, or Young s modulus, is related to many of the mechanical performance characteristics of textile products. The modulus of elasticity can be affected by drawing, ie, elongating the fiber environment, ie, wet or dry, temperature or other procedures. Values for commercial acetate and triacetate fibers are generally in the 2.2—4.0 N/tex (25—45 gf/den) range. 

Crack Tip Stresses. The simplest case for fracture mechanics analysis is a linear elastic material where stress. O, is proportional to strain, S,... 

In moie ductile materials the assumptions of linear elastic fracture mechanics (LEFM) are not vahd because the material yields more at the crack tip, so that... 

Two approaches have been taken to produce metal-matrix composites (qv) incorporation of fibers into a matrix by mechanical means and in situ preparation of a two-phase fibrous or lamellar material by controlled solidification or heat treatment. The principles of strengthening for alloys prepared by the former technique are well estabUshed (24), primarily because yielding and even fracture of these materials occurs while the reinforcing phase is elastically deformed. Under these conditions both strength and modulus increase linearly with volume fraction of reinforcement. However, the deformation of in situ, ie, eutectic, eutectoid, peritectic, or peritectoid, composites usually involves some plastic deformation of the reinforcing phase, and this presents many complexities in analysis and prediction of properties. 

Substantial work on the appHcation of fracture mechanics techniques to plastics has occurred siace the 1970s (215—222). This is based on earlier work on inorganic glasses, which showed that failure stress is proportional to the square root of the energy required to create the new surfaces as a crack grows and iaversely with the square root of the crack size (223). For the use of linear elastic fracture mechanics ia plastics, certaia assumptioas must be met (224) (/) the material is linearly elastic (2) the flaws within the material are sharp and (J) plane strain conditions apply ia the crack froat regioa. 

The importance of inherent flaws as sites of weakness for the nucleation of internal fracture seems almost intuitive. There is no need to dwell on theories of the strength of solids to recognize that material tensile strengths are orders of magnitude below theoretical limits. The Griffith theory of fracture in brittle material (Griflfith, 1920) is now a well-accepted part of linear-elastic fracture mechanics, and these concepts are readily extended to other material response laws. 

Linear Elastic Fracture Mechanics Behavior of Graphite... 

Linear elastic fracture mechanics (LEFM) is based on a mathematical description of the near crack tip stress field developed by Irwin [23]. Consider a crack in an infinite plate with crack length 2a and a remotely applied tensile stress acting perpendicular to the crack plane (mode I). Irwin expressed the near crack tip stress field as a series solution ... 

The basic assumptions of fracture mechanics are (1) that the material behaves as a linear elastic isotropic continuum and (2) the crack tip inelastic zone size is small with respect to all other dimensions. Here we will consider the limitations of using the term K = YOpos Ttato describe the mechanical driving force for crack extension of small cracks at values of stress that are high with respect to the elastic limit. 

Hertzian mechanics alone cannot be used to evaluate the force-distance curves, since adhesive contributions to the contact are not considered. Several theories, namely the JKR [4] model and the Derjaguin, Muller and Torporov (DMT) model [20], can be used to describe adhesion between a sphere and a flat. Briefly, the JKR model balances the elastic Hertzian pressure with attractive forces acting only within the contact area in the DMT theory attractive interactions are assumed to act outside the contact area. In both theories, the adhesive force is predicted to be a linear function of probe radius, R, and the work of adhesion, VFa, and is given by Eqs. 1 and 2 below. 

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