Simple tension

Stress and Distortion. The forces acting on a stmcture are transmitted through the welded joints that is, the joint is subjected to simple tension (or compression), bending, shear, or torsional stresses, or to combinations of these stresses owing to combined loading situations. Weldments must be of a proper size, length, and location to withstand the loads imposed during service. 

Many distribution functions can be apphed to strength data of ceramics but the function that has been most widely apphed is the WeibuU function, which is based on the concept of failure at the weakest link in a body under simple tension. A normal distribution is inappropriate for ceramic strengths because extreme values of the flaw distribution, not the central tendency of the flaw distribution, determine the strength. One implication of WeibuU statistics is that large bodies are weaker than small bodies because the number of flaws a body contains is proportional to its volume. 

This ambiguity in the stress space loading criterion may be illustrated by considering a stress-strain plot corresponding to simple tension, as shown schematically in Fig. 5.3. With each point on the stress-strain curve past the initial elastic limit point A, there is associated a point on the elastic limit surface in stress space and a point on the elastic limit surface in strain space. On the hardening portion of the stress strain curve AB, both the stress and the strain are increasing, and the respective elastic limit surfaces are moving... 

In (8.35) Y is the flow stress in simple tension (and may itself be a function of the temperature and strain rate) and is the critical volumetric strain at void coalescence (calculated within the model to equal 0.15 independent of material). Note that the ductile fragmentation energy depends directly on the fragment size s. With (8.35), (8.30) through (8.32) become, for ideal ductile spall fragmentation,... 

There are four commonly occurring states of stress, shown in Fig. 3.2. The simplest is that of simple tension or compression (as in a tension member loaded by pin joints at its ends or in a pillar supporting a structure in compression). The stress is, of course, the force divided by the section area of the member or pillar. The second common state of stress is that of biaxial tension. If a spherical shell (like a balloon) contains an internal pressure, then the skin of the shell is loaded in two directions, not one, as shown in Fig. 3.2. This state of stress is called biaxial tension (unequal biaxial tension is obviously the state in which the two tensile stresses are unequal). The third common state of stress is that of hydrostatic pressure. This occurs deep in the earth s crust, or deep in the ocean, when a solid is subjected to equal compression on all sides. There is a convention that stresses are positive when they pull, as we have drawn them in earlier figures. Pressure,... 

We can now define the elastic moduli. They are defined through Hooke s Law, which is merely a description of the experimental observation that, when strams are small, the strain is very nearly proportional to the stress that is, they are linear-elastic. The nominal tensile strain, for example, is proportional to the tensile stress for simple tension... 

Not only are there two classes of deformation, there are also two modes in which deformation can be produced simple shear and simple tension. The actual action during melting, as in the usual screw plasticator is extremely complex, with all types of shear-tension combinations. Together with engineering design, deformation determines the pumping efficiency of a screw plasticator and... 

In order to apply the crack nucleation approach, the mechanical state of the material must be quantified at each point by a suitable parameter. Traditional parameters have included, for example, the maximum principal stress or strain, or the strain energy density. Maximum principal strain and stress reflect that cracks in rubber often initiate on a plane normal to the loading direction. Strain energy density has sometimes been applied as a parameter for crack nucleation due to its connection to fracture mechanics for the case of edge-cracked strips under simple tension loading. ... 

Several criticisms of these parameters have recently been pointed out. First, they have no specific association with a material plane (i.e., they are scalar parameters), despite the fact that cracks are known to nucleate on specific material planes. With traditional parameters it is difficult to account for the effects of crack closure under compressive loading. Traditional parameters have not been successful at unifying experimental results for simple tension and equibiaxial tension fatigue tests. Finally, a nonproportional loading history can always be constmcted for a given scalar equivalence parameter that holds constant the value of the scalar parameter, but which results in cyclic loading of material planes. For such histories, scalar parameters incorrectly predict infinite fatigue life. 

It is useful to get preliminary learning on the mechanical properties of materials under simple static tension. Members of engineering structures are often subjected to steady axial loads in tension. Moreover, the response of materials subjected to other types of loading also can often be explained or predicted on the basis of knowledge of their behaviour under simple tension. In addition, such behaviour is usually quite easy to study experimentally. 

Maximum principal stress theory which postulates that a member will fail when one of the principal stresses reaches the failure value in simple tension, or. The failure point in a simple tension is taken as the yield-point stress, or the tensile strength of the material, divided by a suitable factor of safety. 

Maximum shear stress theory which postulates that failure will occur in a complex stress system when the maximum shear stress reaches the value of the shear stress at failure in simple tension. 

The samples were tested at a deformation rate of 1 in./min. for the simple tension experiments. In the case of stress-relaxation measurements, the samples were prestrained to 7% elongation at e = 5 in./min. then allowed to stress relax over a 20 minute period. All mechanical testing were carried out at room temperature. 

Figure 1. Stress-time data from stress-strain curves measured in simple tension at 30°C on the LHT-240 polyurethane elastomer at seven extension rates, A from 9.4 X t° 9.4 min 1. Key 0,9, stress as a function of time ( — 1)/X, at the indicated values of strain, ( — 1).

Background. Consider that pairwise interactions between active network chains (13), commonly termed trapped entanglements, do not significantly affect the stress in a specimen deformed in simple tension or compression. Then, according to recent theory (16,17), the shear modulus for a network in which all junctions are trifunctional is given by an equation which can be written in the form (13) ... 

Moreover, for deformations other than simple tension the apparent Pojs-son s ratio -tr/ is a function of the type of deformation. 

The hyperbolic sine function also fits many experimental simple tension data, and it has considerable theoretical foundation (77-88) ... 

One of the simplest criteria specific to the internal port cracking failure mode is based on the uniaxial strain capability in simple tension. Since the material properties are known to be strain rate- and temperature-dependent, tests are conducted under various conditions, and a failure strain boundary is generated. Strain at rupture is plotted against a variable such as reduced time, and any strain requirement which falls outside of the boundary will lead to rupture, and any condition inside will be considered safe. Ad hoc criteria have been proposed, such as that of Landel (55) in which the failure strain eL is defined as the ratio of the maximum true stress to the initial modulus, where the true stress is defined as the product of the extension ratio and the engineering stress —i.e., breaks down at low strain rates and higher temperatures. Milloway and Wiegand (68) suggested that motor strain should be less than half of the uniaxial tensile strain at failure at 0.74 min.-1. This criterion was based on 41 small motor tests. 

As the stored energy is the area under the stress-strain curve, we can derive the stress-strain curve predicted by this phenomenological model from the differential of W relative to strain. In simple tension this comes to ... 

If the material is linear and elastic then the applied stress a is directly proportional to the strain e. Then for simple tension ... 

The tensile yield stress variation as a function of W for a material which has a von Mises-type yield locus is illustrated schematically in Figure 5. This variation is caused by the fact that as the width of the specimen increases, the biaxiality also increases toward the asymptotic value at plane strain. If the material obeys the von Mises yield criterion exactly, the plane strain yield stress should be 15% higher than it would be for simple tension. On the other hand, if the material obeys the Tresca yield criterion, the plane strain yield stress should be identical... 

In non-dispersive systems, such as acoustic waves in a fluid or simple tension waves on a string, the wave speed does not vary with frequency. Thus the energy speed Cg is the same as the phase speed c, so that... 

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