API TR 10TR7 pdf free download

API TR 10TR7 pdf free download.Mechanical Behavior of Cement.
4.4 Elasticity General 4.4.1 Elasticity is the property of a material to return to its original shape when unloaded. Elastic deformation is reversible. Linear elasticity is a material property to deform elastically and proportionally to stress: stress–strain curves are linear. Elastic Limit 4.4.2 The elastic limit is the stress or deformation limit where the material transitions from elastic behavior to nonelastic behavior. The elastic limit is not necessarily associated with sample failure as defined in 4.5, 4.6, or 4.9 and can be related to irreversible behavior due to plasticity, for example. Elastic Constants 4.4.3 4.4.3.1 General Many elastic materials have a tendency to deform linearly (or approximately linearly) as long as the stress does not exceed the material’s elastic limit. This linear-elastic behavior is described by Hooke’s law, which states that strain is a linear function of stress. Elastic constants, which represent the material’s elastic properties, are conveniently defined to link stress and strain. Some of the most commonly used elastic constants are Young’s modulus, Poisson’s ratio, shear modulus, and bulk modulus. For isotropic materials, the material’s elastic properties are fully described by any two of these elastic constants (all the others can be calculated theoretically). At moderate stress levels cement can be assumed to exhibit linear-elastic behavior and therefore its elastic constants are often reported. Young’s, shear, and bulk moduli are typically expressed in gigapascals (GPa) or pounds-force per square inch (psi).4.4.3.2 Determination of Elastic Properties All elastic properties can be determined in several ways when the stress–strain curves like the one in Figure 4 are not fully linear, as follows. — Tangent: determined from linear regression on the stress–strain test data over a stress range (see Figure 4A).— Chord: the slope of a line connecting any two points on the stress–strain curve (see Figure 4B). — Secant: the slope of a line from any point on the stress–strain curve relative to the zero stress point (uniaxial test) or zero net stress point (triaxial test) (see Figure 4C). The secant is the least preferred method because the stress–strain curve may not be linear near zero stress. For a perfectly linear-elastic material, tangent, secant, and chord Young’s parameters are all identical. However, the experimental determination of all the elastic parameters should be made over the same stress range. The elastic properties can be determined while the sample is being loaded (as shown in the Figure 4 example) or unloaded (not shown). The range used for determining the tangent or chord modulus can be prescribed, for example: 25 % to 40 %, or 1 0 % to 50 % of the axial stress to maximum stress before failure. However, the end user should use a range close to the value that the information will be used and that the sample exhibits linear behavior.Mohr found that the transformation equation relating the shear and normal stresses takes the form of a circle. Once this “Mohr’s circle” is defined, the stress at a point is fully understood. This concept is important for cement testing because physical observations of failed specimens subjected to normal stresses are often found to fail in shear. This is especially true when cement is tested in a confined state. The normal stresses at the time of failure are points on the x-axis. API TR 10TR7 pdf download.