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An elastic modulus also known as modulus of elasticity is a quantity that measures an object or substance's resistance to being deformed elastically i. The elastic modulus of an object is defined as the slope of its stress—strain curve in the elastic deformation region: [1] A stiffer material will have a higher elastic modulus. An elastic modulus has the form:.
The estimation of the in situ stresses is very crucial in oil and gas industry applications. Prior knowledge of the in situ stresses is essential in the design of hydraulic fracturing operations in conventional and unconventional reservoirs. The fracture propagation and fracture mapping are strong functions of the values and directions of the in situ stresses. Other applications such as drilling require the knowledge of the in situ stresses to avoid the wellbore instability problems. The laboratory values are then used to correlate the dynamic values derived from the logs.
Stress and strain may be described as follows in the case of a metal bar under tension. If a metal bar of cross-sectional area A is pulled by a force F at each end, the bar stretches from its original length L 0 to a new length L n. Simultaneously the cross section decreases. Strain is dimensionless. The value for steel is about three times greater, which means that it takes three times as much force to stretch a steel bar the same amount as a similarly shaped aluminum bar. As stresses increase, the material may either flow, undergoing permanent deformation, or finally break. When a metal bar under tension is elongated, its width is slightly diminished.
The stress at which the linear relationship between stress (1) Linear elasticity called Young's modulus, corresponding to linear strain. (2) Elasticity of (3) Elasticity of shape or shear modulus or Modulus of Rigidity, corresponding to shear strain. (α) and the ratio between them is a constant, called Poisson's ratio (σ). .
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When a sample of material is stretched in one direction it tends to get thinner in the lateral direction - and if a sample is compressed in one direction it tends to get thicker in the lateral direction. Strain is defined as "deformation of a solid due to stress". An aluminum bar with length 10 m and radius mm 10 -3 m is stretched 5 mm 5 10 -3 m. The radial contraction in lateral direction can be calculated by combining eq.
It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. For a fluid , only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper , these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law.
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The derived SI unit of shear modulus is the pascal Pa , although it is usually expressed in gigapascals GPa or in thousand pounds per square inch ksi. The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law :. The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force such as friction. In the case of an object shaped like a rectangular prism, it will deform into a parallelepiped. Anisotropic materials such as wood , paper and also essentially all single crystals exhibit differing material response to stress or strain when tested in different directions. In this case, one may need to use the full tensor-expression of the elastic constants, rather than a single scalar value.
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Young's Modulus And Bulk Modulus relation · K is the Bulk modulus. · Y is Young's modulus. · μ is the Poisson's ratio.
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ReplyBulk and shear modulus, and Poisson's ratio, for polystyrene and apparent conﬂict between the classic elastic equations and the experiments. dynamic compressibility of a rubber-sulfur vulcanizate and its relation to free.
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