Residual stresses are generated, upon equilibrium of material, after plastic deformation that is caused by applied mechanical loads, thermal loads, or phase changes. Mechanical and thermal processes applied to a component during service may also alter its residual stress state.

Welding residual stresses are caused by differential thermal expansion and contraction of the weld metal and parent material. This is illustrated in Fig. 7.5 for longitudinal residual stresses (transverse residual stresses are also induced, although these generally have compressive and tensile zones within the weld).

Residual stresses are those stresses that remain in an object (in particular, in a welded component) even in the absence of external loading or thermal gradients. In some cases, residual stresses result in significant plastic deformation, leading to warping and distortion of an object.

The development of residual thermal stress in a “free-quenching” part due to variations in cooling across the molded part and the material’s response to the temperature history. Variation in the cooling rate from the mold wall to its center can cause thermal-induced residual stress.

The thermal method involves changing the temperature of the entire part uniformly, either through heating or cooling. When parts are heated for stress relief, the process may also be known as stress relief bake. Cooling parts for stress relief is known as cryogenic stress relief and is relatively uncommon.

Hole drilling is the most commonly used stress relaxation technique for measuring residual stresses. Stressed material is removed by drilling a small blind hole in the area of interest and the material around the hole spontaneously finds a new stress equilibrium.

Using laboratory-based or portable equipment, the XRD technique measures surface residual stresses to depths of up to 30μm by measuring the material’s inter-atomic spacing.

Compressive residual stresses are induced at the surface by the impingement of the shot, effectively cold working it through plastic deformation, visually evident by a series of overlapping dimples.

Stress is the ratio of force over area (S =F/A, where S is stress, F is the external force or load and A is the cross-sectional area). Strain is the ratio of change in length to the original length, when a given body is subjected to some external force (Strain= change in length÷the original length).

Stress is the a measure of what the material feels from externally applied forces. Forces that are applied perpendicular to the cross section are normal stresses, while forces applied parallel to the cross section are shear stresses.

No, stress is not a property of a material. Stress is simply THE RESISTANCE OFFERED BY A BODY to external force applied on it.

The basic material properties that need to be known for accurate finite element analysis are:

• Young’s modulus of elasticity and yield strength.
• Bulk and shear modulus.
• Poisson’s ratio.
• Density.

These material models are used when an elastic material is going to be loaded past the yield strength of the material. When this happens, plastic deformation will occur. The “von Mises with – Hardening” material model will use a bilinear curve to calculate the stress values.

Whenever the material is changed, it gives me different stress result for every different materials… Hooke’s Law stated that E=Stress/Strain… Next, stress is material independent when in elastic region but material dependent in plastic region…

Material nonlinearity involves the nonlinear behavior of a material based on a current deformation, deformation history, rate of deformation, temperature, pressure, and so on. Examples of nonlinear material models are large strain (visco) elasto-plasticity and hyperelasticity (rubber and plastic materials).

Nonlinearities are classified into three major types: Geometric nonlinearities. Material nonlinearities. Contact nonlinearities.

Linear optics is a sub-field of optics, consisting of linear systems, and is the opposite of nonlinear optics. If monochromatic light enters an unchanging linear-optical system, the output will be at the same frequency. For example, if red light enters a lens, it will still be red when it exits the lens.

In enantioselective synthesis, a non-linear effect refers to a process in which the enantiopurity of the catalyst or chiral auxiliary does not correspond with the enantiopurity of the product produced. Non-linear effects often arise in reactions with a scalemic catalyst composition.

CANOVA and MIC can both be used to test nonlinear correlation; however, CANOVA has its own advantages. While MIC tests all types of non-random correlations, CANOVA tests the alterative hypothesis that “similar X values lead to similar Y values”.

A linear relationship can also be found in the equation distance = rate x time. Because distance is a positive number (in most cases), this linear relationship would be expressed on the top right quadrant of a graph with an X and Y-axis.

Plot the equation as a graph if you have not been given a graph. Determine whether the line is straight or curved. If the line is straight, the equation is linear. If it is curved, it is a nonlinear equation.

Linear text refers to traditional text that needs to be read from beginning to the end while nonlinear text refers to text that does not need to be read from beginning to the end. As their names imply, linear texts are linear and sequential while non-linear and non-sequential.

If a, b, and r are real numbers (and if a and b are not both equal to 0) then ax+by = r is called a linear equation in two variables. (The “two variables” are the x and the y.) The numbers a and b are called the coefficients of the equation ax+by = r.

In the case of linear equations, the graph will always be a line. In contrast, a nonlinear equation may look like a parabola if it is of degree 2, a curvy x-shape if it is of degree 3, or any curvy variation thereof. While linear equations are always straight, nonlinear equations often feature curves.

A linear equation is always a polynomial of degree 1 (for example x+2y+3=0). In the two dimensional case, they always form lines; in other dimensions, they might also form planes, points, or hyperplanes. Their “shape” is always perfectly straight, with no curves of any kind. This is why we call them linear equations.

It is made up of two expressions set equal to each other. A linear equation is special because: It has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.

Simply put, a linear equation draws a straight line on a regular x-y graph. The equation holds two key pieces of information: the slope and the y-intercept. The slope’s sign tells you if the line rises or falls as you follow it left to right: A positive slope rises, and a negative one falls.