Biaxial stress state

During the optical coat work stress examination method the upper plate of the head of some of the bolts was covered with an optical coat work (Fig. 4). On the head of some other bolts strain gauges were stuck which measured the plain biaxial stress state in the middle of the top surface of the head of the bolt (3.5 x 3 mm). The magnetic probe detected average stresses up to 0.1 mm depth in an area of 14 mm diameter in the middle of the head of the bolt. 

Now that the basic stiffnesses and strengths have been defined for the principal material coordinates, we can proceed to determine how an orthotropic lamina behaves under biaxial stress states in Section 2.9. There, we must combine the information in principal material coordinates in order to define the stiffness and strength of a lamina at arbitrary orientations under arbitrary biaxial stress states. 

CA 63,17781 (1965) Proplnt failure characteristics were measured in uniaxial and biaxial stress states for poly butadiene acrylic acid and Nitroplastisol proplnts, and failure conditions were examined over a wide range of temps. The observed failure conditions were compared for various failure criteria, and it was found that a... 

The [10°] off axis tension specimen shown in Fig 3.23 is another simple specimen similar in geometry to that of the [ 45 ]s tensile test. This test uses a unidirectional laminate with fibers oriented at 10° to the loading direction and the biaxial stress state (i.e. longitudinal, transverse and in-plane shear stresses on the 10° plane) occurs when it is subjected to a uniaxial tension. When this specimen fails under tension, the in-plane shear stress, which is almost uniform through the thickness, is near its critical value and gives the shear strength of the unidirectional fiber composites based on a procedure (Chamis and Sinclair, 1977) similar to the [ 45°]s tensile test. 

A more convenient means of representing general biaxial stress states is obtained by introducing a variable defined as ... 

The stress state variable >fr is depicted in Figure 2 and has the following important special values = 45° represents equal biaxial tension 0° and 90° uniaxial tension —90° and 180° uniaxial compression —45° and 135° pure shear and —135° equal biaxial compression. All biaxial stress states can be represented by a range of values from 45° to —135°. 

Figure 2. Designation of general biaxial stress states in terms of a stress state angle variable and magnitude S = y/St2 + S22. is defined by tan St/Si).

Figure 4. Maximum algebraic stress concentrations developed in general biaxial stress states defined by P of Figure 2...

Fig. 10.28. Sequence of snapshots of martensitic microstructnre corresponding to different load levels (courtesy of R. James and C. Chu) as obtained using polarized hght. Different shades correspond to different variants of the Cu-Al-Ni martensite. Biaxial stress state applied using machine shown in fig. 10.27, with stresses applied along (Oil) and (Oil) directions (a) =...

The numerical model we used was originally developed by Gill and Clyne [6] and has been modified to handle multi-layered deposits. It is a 1-dimensional model and consists of two parts thermal profile calculation and stress calculation. By regarding the torch motion as a fluctuation in the heat and mass flux onto a reference point on the substrate and assuming biaxial stress state, the program calculates both the through-thickness thermal profile and stress distribution during thermal spray as functions of time. 

Figure 6.29 Comparison of von Mises and Tresca yield criteria for biaxial stress states.

Eigure 1-4 is an overlay of Figures 1-1,1-2, and 1-3 and will illustrate the major differences between the three theories. For the case of biaxial stress state, all three theories are in agreement where their bounded areas graphically overlap. The bounded area by each theory indicates the elastic range of which there is no yielding, however, it is important to note that in quadrants II and IV that the maximum principal stress theory provides unconservative results. For example, consider point B at the midpoint of the line in Figure 1-2. It shows shear stress is equal to ((72 - (-<7i))/2, which equals (<72 -I- (7i)/2 or one-half the stress which would... 

D.K. Shetty, A.R. Rosenfield, and W.H. Duckworth (1987), "Mixed-Mode Fracture in Biaxial Stress State Application of the Diametral-Compression (Brazilian Disk) Test," Eng. Fract. Mech., 26, 6, 825-39. 

GAPD s approach consists of materials characterization and behavior modeling, combined with component analysis and risk integration tools. Uniaxial and biaxial stress states will be evaluated to develop models for fast fracture, slow crack growth, creep deformation, and oxidation. The accuracy of the methodology will be verified by testing simulated components under stress and temperature conditions representative of gas turbine engine operation. 

To understand the essential differences between the Tresca and von Mises criteria let us consider the simplified case of a biaxial stress state, where we assume that the principal stress, is zero. 

API 620 tanks tend to be more complicated in geometry and are generally subjected to higher internal pressure than API 650 tanks. Accordingly, the requirements of API 620 differ significantly from those of API 650 because the thickness of the components is obtained from stress analysis that considers the biaxial stress state rather than a set of simplified formulas. 

Fig. 3.48 a Stress distribution on a circular section subjected to a pure torsional moment T. b elemental free body taken at any point in the bar which shows the biaxial stress state generated by pure shearing-stress... 

Fig. A.10 Analogy between the biaxial stress state in a pressure vessel wall and that existing ahead of the crack tip in a WOL-X or WOL-T or compact C(T)...

The constitutive behavior of masonry under biaxial states of stress cannot be completely described from the ccmstitutive behavior under uiuaxial loading conditions. The influence of the biaxial stress state has been investigated up to peak stress to provide a biaxial strength envelope, which cannot be described solely in terms of principal stresses because masonry is an anisotropic material. Therefore, the biaxial strength envelope of masonry must be described either in terms of the full stress vector in a fixed set of... 

The Arcan and losipescu specimens can also be used as a joint where the adhesive is in a thin layer between two substrates. The test methodology is very similar to the bulk version. The adhesive displacement can be measured by noncontacting devices or extensometers of the type proposed by Dean et al. (1996). For devices that measure the adhesive and adherend displacement, a correction must be applied to have only the adhesive displacement. The stress distribution is not perfectly uniform, and an FE analysis can be used to have the value at the center of the specimen where the strain is obtained. Grabovac and Morris (1991) and Wycherley et al. (1990) used the losipescu method where two shaped adherends are bonded together. Weissberg and Arcan (1988) proposed a joint test based on the Arcan configuration. More recently, Cognard et al. (2005) proposed an Arcan joint method to produce not only shear but also biaxial stress states. 

Kody RS, Lesser AJ (1999) Yield behavior and energy absorbing characteristics of rubber-modified epoxies subjected to biaxial stress states. Polym Compos 20 250... 

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