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Stress is an internal force extended by either of two adjacent parts of a body upon the other across an imagined plane of separation. When the forces are parallel to the plane, the stress is called shear stress; when the forces are normal to the plane, the stress is called normal stress; when the normal stress is directed towards the part on which it acts, it is called compressive stress; and when it is directed away from the part on which it acts, it is called tensile stress. Shear, compressive, and tensile stresses, respectively, resist the tendency of the parts to mutually slide, approach, or separate under the action of applied forces.
When performing engineering analysis, we are always concerned with how a body will behave under external loading. Newton’s laws, or the laws that most generally govern this behavior, are:
First Law: A body will remain at rest or will continue its straight line motion with constant velocity if there is no unbalanced force acting on it.
Second Law: The acceleration of a body will be proportional to the resultant of all forces acting on it and in the direction of the resultant.
Third Law: Action and reaction forces between interacting bodies will be equal in magnitude, collinear, and opposite in direction.
The most important engineering equation arising from these laws follows:
F = ma
were F is the resultant force vector, m is the mass of the body under consideration, and a is its acceleration vector.
The most useful tool for understanding and implementing the loads and constraints, or boundary conditions that govern a body’s behavior, is the free body diagram. The general free body diagram represents the body in space removed from its operating system. If the body is in equilibrium, all externally applied loads and reaction forces must add up to zero, both in magnitude and direction.
The FEA method, used to analyze structure and obtain stress distribution, is involve cutting a structure into several elements, describing the behavior of each element in a simple way, then reconnecting elements at "nodes".
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Casting analysis can be beneficial from an economic standpoint by reducing repairs and scrapped castings. Analysis can be beneficial from a quality standpoint by predicting likely defects that may be avoided with the casting or mold design change. Casting analysis tools have allowed the field of casting design to move from trial and error to a rational process.
An objective of thermal analysis is to track the temperature distribution in the aluminum die-casting and the mold during the solidification process. This is transient heat transfer analysis. The result of this analysis is used to optimize both part design and die cooling system.
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Modal or natural frequency analyses are used frequently when parts being design or verified are subject to vibration or cyclic loads. This solution type returns the resonant frequencies for a given structure under a specified constraint set. The mode shapes corresponding to those frequencies are also provided. Modal analysis is extremely important for product mounted on an engine that experience vibration resulting from the engine’s unbalanced forces.
The goal of a modal study is to ensure that the system does not have a resonant frequency near the operating frequency or in the range of operating frequencies.
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Warpage analysis is the next step in developing part and mold design for a die casting process.
Warpage analysis starts at the point of ejection from the mold because, prior to that, it would be even more difficult to assume that the material properties, primarily stiffness, would be constant. The applied ambient load is the expected temperature drop between the part’s temperature at mold ejection and room temperature. Contraction response of the casting is used to evaluate potential problems.
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A FE analysis can pinpoint high stresses in a part or assembly, but that location might not be where cracks first initiates or failure occurs. In the real world, most parts experience cyclical loads which makes them fail from fatigue.
Fatigue is a tendency of materials to fracture under many repetitions of a stress considerably less than the ultimate static strength.
Several methods are available to relate cyclic loading data to fatigue life. The most generally accepted of which is expressed by Goodman diagram. In each cycle the stress varies from a maximum value Gmax to a minimum value Gmin, either of which is plus or minus according to whether it is tensile or compressive.
The mean stress is:
Gm = ½(Gmax + Gmin )
and the alternating stress is:
Ga = ½(Gmax - Gmin )
the addition and subtraction being algebraic. With reference to rectangular axes, Gm is measured horizontally and Ga vertically. When Gm = 0, the limiting value of Ga is the endurance limit for fully reversed stress, denoted here by A. Endurance limit is defined as the maximum cyclic stress which a part can sustain for an "infinite" number of cycles. When Ga = 0, the limiting value of Gm is the ultimate tensile strength, denoted here by B.
According to the Goodman theory, the ordinate to a point on the straight line AB represents the maximum alternating stress Ga that can be imposed in conjunction with the corresponding mean stress Gm. Any point above AB line represent a stress condition that would eventually caused failure. Any point below AB represents a stress condition with more or less margin of safety.
References:
- W.C.Young, Roark's Formulas for Stress and Strain, 6th ed., McGraw-Hill, New York, 1989.
- R.D.Cook, Finite Element Modeling For Stress Analysis,Lohn Wiley & sons, INC., New York, 1994.
- V.Adams and A.Askenazi, Building Better Products with Finite Element Analysis, OnWord Press, Santa Fe, 1998
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