Atlas of stress strain curves

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Eq 34 Eq 35 so that at a point of tensile instability: d 0. Also, it may be convenient to use the compression test because the specimen is relatively easy to make, and it does not require a large amount of material.

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The compression test is frequently used in conjunction with evaluating the workability of materials, especially at elevated temperature, because most deformation processes, such as forging, have a high component of compressive stress. The test is also used with brittle materials, which are difficult to machine into test specimens and difficult to tensile test in perfect alignment. There are two inherent difficulties with the compression test that must be overcome by the test technique: buckling of the specimen and barreling of the specimen.

Both conditions cause nonuniform stress and strain distributions in the specimen that make it difficult to analyze the results. The tensile elongation is then: Lf-Lo a M M Eq 41 This clearly indicates that the total elongation is a function of the specimen gage length. The shorter the gage length, the greater the percent elongation.

Numerous attempts have been made to rationalize the strain distribution in the tension test. Perhaps the most general conclusion that can be drawn is that geometrically similar specimens develop geometrically similar necked regions. Notch Tensile Test. Ductility measurements on standard smooth tensile specimens do not always reveal metallurgical or environmental changes that lead to reduced local ductility. The tendency for reduced ductility in the presence of a triaxial stress field and steep stress gradients such as a rise at a notch is called notch sensitivity.

A common way of evaluating notch sensitivity is a tension test using a notched specimen. Buckling is a mode of failure characterized by an unstable lateral material deflection caused by compressive stresses. Buckling is controlled by selecting a specimen geometry with a low length-to-diameter ratio. It also is important to have a very well-aligned load train and to ensure that the end faces of the specimen are parallel and perpendicular to the load axis Ref Often a special alignment fixture is used with the testing machine to ensure an accurate load path Ref Barreling is the generation of a convex surface on the exterior of a cylinder that is deformed in compression.

The cross section of such a specimen is barrel shaped. Barreling is caused by the friction between the end faces of the compression specimen and the anvils that apply the load. Source: Ref 30 0. Curve 1, molygrease; curve 2, Molykote spray; curve 3, boron-nitride spray; curve 4, boron-nitride and alcohol; curve 5, Teflon and Molykote spray; curve 6, polished dry anvils; curve 7, grooved anvils. Source: Ref 30 Fig.

Atlas of Stress-Strain Curves (#06825G)

The calculation of stress and strain for the compression test is based on developing a test condition that minimizes friction and barreling and assumes the stress state is axial compression. In Eq 43, subscript 1 refers to the initial values of D and h, while subscript 2 refers to conditions at some subsequent value of specimen height, h. Equation 43 shows that the flow stress can be obtained directly from the load P and the instantaneous height Q12 , provided that friction can be neglected. The true strain in the compression test is given by: Eq 44 where either the displacement of the anvil or the diameter of the specimen can be used, whichever is more convenient.

Compressive tangent modulus, psi Fig, 1 6 10 12 Curve combining compressive stress-strain with compressive tangent modulus As the material spreads outward over the anvils, it is restrained by the friction at this interface.

Atlas of Stress-Strain Curves

The material near the midheight position is less restrained by friction and spreads laterally to the greatest extent. The material next to the anvil surfaces is restrained from spreading the most; thus, the creation of a barreled profile. This deformation pattern also leads to the development of a region of relatively undeformed materials under the anvil surfaces. This deformation behavior clearly means that the stress state is not uniform axial compression.

In addition to the axial compressive stress, a circumferential tensile stress develops as the specimen barrels Ref Because barreling increases with the specimen ratio DJh, the force to deform a compression cylinder increases with DIh. Minimizing barreling of the compression specimen can be accomplished by minimizing friction between the ends of the specimen and the anvils. This is done by using an effective lubricant and machining concentric rings on the end of the specimen to retain the lubricant and keep it from being squeezed out. An extensive series of tests have shown what works best Ref Figure 14 shows the true stress-true strain curve flow curve for an annealed Al-2Mg alloy.

Stress and strain were calculated as described in the previous section. Note how the flow curve in compression agrees with that determined in a tensile test and how the compressive curves extend to much larger strains because there is no specimen necking. Figure 15 extends the strain over double the range of Fig. The highest curve greatest deviation from uniaxial stress is for grooved anvils platens that dig in and prevent sidewise flow.

Atlas of Stress-Strain Curves Second Edition yflSNV

The least friction is for the condition where a Teflon E. A M Strain e Strain E a pjcr 1 7 b Differences between constant stress increments and constant strain increments, a Equal stress increments result in strains of increasing increments, b Equal strain increments result in decreasing stress increments. These parameters are given to the extent that they are available. Test Temperature. Relative to room-temperature RT tests, most materials become stronger, but less ductile, at lower temperatures, and more ductile, but weaker, at higher temperatures.

There are anomalous behaviors such as blue brittleness.

Strain-rate and temperature-dependent stress-strain curves of Sn-Pb eutectic alloy | SpringerLink

Because such temperatures produce a bluish temper color on the surface of the specimen, this problem has been called blue brittleness. Typically, brittleness is associated with cold-temperature behavior.

Speed of Test. Greater strain rates 10 -1 and s - 1 are considered dynamic tests.

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However, if the deformation is nonhomogeneous, then the strain and strain rate varies the specimen length, and the specific deformation rate represents the spatial average strain rate. A well-known example of nonhomogeneous deformation is the propagation of deformation bands called Liiders bands. Stress Rate. Figure 17 illustrates the differences in curves constructed from constant stress increments and constant strain increments.

Slow Speeds. Under relatively slow straining, most materials are assumed to transfer the heat generated by plastic deformation to their surroundings; that is, the straining is assumed to be isothermal no change of temperature.

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The degree to which slow tension tests remain truly isothermal has been investigated Ref The flow stress, which is the uniaxial stress needed to continue plastic deformation of the material at a given stage of a test, is then assumed to depend only on strain and strain rate. The strain-hardening parameter n has been defined.

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From Eq dz Eq 47 In an analogous manner, the strain-rate sensitivity parameter m can be defined as: e do a dk Eq 48 Both n and m are functions of strain and strain rate, m can be negative under some conditions. However, average values frequently are selected for these parameters, which are then treated as constants. Values of n usually are between 0. Under such conditions, these materials can be deformed to extremely large strains and are called superplastic metals. High Rate Testing.

For extremely high rates of testing, it is commonly assumed that deformation occurs under adiabatic no heat transfer conditions. The remainder is inelastically stored as changes in defect structure. In high-speed tests, this heat raises the temperature of the material. Consequently, the material properties are changed. This is another major complication in analyses of high-speed tests. Consequences of testing over a wide spectrum of strain rates are summarized in Fig. If a specimen is loaded past its yield point and then unloaded, or loaded in reverse, subsequent testing on the specimen would result in a different pattern of behavior.

Figure 19 shows this effect. The specimen is loaded initially to point A. The solid line represents the behavior of the virgin sample. If instead, the sample were unloaded at point A, the path of unloading is parallel to the initial load path dotted line. There is some permanent deformation residual strain , and the area is redetermined as A2. When reloaded, the dotted line is retraced and the yield point is now higher due to strain hardening. If this unloading and reloading were done again at point B, the dashed line indicates the behavior. Figure 19 illustrates the effect of stopping and restarting a test.

It also points to a consideration when a test sample is machined from a failed part. If the testpiece were subjected to deformation prior to the failure, the properties obtained from the test should not be equated to the original material properties Ref If the prior history of the test specimen includes compression, a hysteresis is present, know as the Bauschinger effect.

This is illustrated in Fig. On unloading and reloading in tension, the shape of the stress-strain curve is significantly different than the original. Again the prior deformation of a test sample will affect its behavior Ref Figure 21 shows the two types of hysteresis possible in titanium alloys, one with load reversal, and one with load application, rest, and reapplication. Nature of Loading.

Figure 22 illustrates a stress-strain loop under controlled constant-strain cycling in a low-cycle fatigue test. During initial loading, the stress-strain curve is O-A-B, with yielding beginning about A. Upon unloading, yielding begins in compression at a lower stress C due to the Bauschinger effect In reloading in tension, a hysteresis loop develops. The dimensions of this loop are described by its width As the total strain range and its height Aa the stress range. The width of the hysteresis loop depends on the level of cyclic strain.

Various Stress Strain Curves! - Lecture - 3