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In solid mechanics, the tangent modulus is the slope of the stress–strain curve at any specified stress or strain. Below the proportional limit (the limit of the linear elastic regime) the tangent modulus is equivalent to Young's modulus. Above the proportional limit the tangent modulus varies with strain and is most accurately found from ...
Isostatics or stress trajectories [7] are a system of curves which are at each material point tangent to the principal axes of stress - see figure [8] Isoclinics are curves on which the principal axes make a constant angle with a given fixed reference direction. These curves can also be obtained directly by photoelasticity methods.
It can therefore also be formulated in terms of a plot of true stress against nominal strain. On such a plot, necking will start where a line from the point ε N = –1 forms a tangent to the curve. This is shown in the next figure, which was obtained using the same Ludwik-Hollomon representation of the true stress – true strain relationship ...
A schematic diagram for the stress–strain curve of low carbon steel at room temperature is shown in figure 1. There are several stages showing different behaviors, which suggests different mechanical properties. To clarify, materials can miss one or more stages shown in figure 1, or have totally different stages.
After the stress distribution within the object has been determined with respect to a coordinate system (,), it may be necessary to calculate the components of the stress tensor at a particular material point with respect to a rotated coordinate system (′, ′), i.e., the stresses acting on a plane with a different orientation passing through ...
Subsequent deformation requires a stress that varies linearly with the strain observed, the slope of the graph of stress vs. strain is the modulus of elasticity, as usual. The work-hardened steel bar fractures when the applied stress exceeds the usual fracture stress and the strain exceeds usual fracture strain.
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To describe the stress relaxation behaviour, one can also consider another three-parameter model more suited to the stress relaxation experiment, consisting of a Maxwell unit placed in parallel with a spring. Its differential stress–strain equation is the same as the other model considered, therefore the two models are equivalent.