Elastic stress analysis

Elastic Behavior The assumption that displacement strains will produce proportional stress over a sufficiently wide range to justify an elastic-stress analysis often is not valid for nonmetals. In brittle nonmetallic piping, strains initially will produce relatively large elastic stresses. The total displacement strain must be kept small, however, since overstrain results in failure rather than plastic deformation. In plastic and resin nonmetallic piping strains generally will produce stresses of the overstrained (plasfic) type even at relatively low values of total displacement strain. 

Creep and stress relation Creep and stress relaxation behavior for plastics are closely related to each other and one can be predicted from knowledge of the other. Therefore, such deformations in plastics can be predicted by the use of standard elastic stress analysis formulas where the elastic constants E and y can be replaced by their viscoelastic equivalents given in Eqs. 2-19 and 2-20. 

Naim [178] performed linear elastic stress analysis of residual stresses in unidirectional high-performance composites containing high-modulus fibers and an interphase region. Naim and Zoller [179] provided data for composites with thermoset and thermoplastic matrices, and showed by linear elastic stress analysis how the buildup of residual thermal stresses during fabrication is related to the disparate thermal expansion properties of the fibers and matrices. 

The shrinkage in the glassy temperature region and the internal stress both depended on the difference between Tg and the measurement temperature. Townsend et al [181] presented a general theory for the elastic interactions in a composite plate of layers with different relaxed planar dimensions. Bauchiere et al [182] measured the thermally induced stresses in epoxyglass bilayers and correlated the results by using Equation 11.45 which is based on linear elastic stress analysis. In this equation, t is the thickness, T[Pg.480]

With respect to the W-type radiant tube used in the above noted comparative test, stress analysis was carried out in order to investigate the mechanical strength of the radiant tube. The method adopted is a Three Dimensional Elastic Stress Analysis using FEM ANSYS version 9, where the self-weight, measured temperature profile and assumed tube inside pressure at extraordinary combustion are considered. In the thermal stress analysis the measured tube surface temperature at 20 points, which seems to be timely, steady state was used as a smooth temperature curve over the measuring... 

The established standard test method for CF crack growth rate is ASTM E647 (30). In this constant load test method, the crack length is measured visually as a function of elapsed cycles followed by numerical analysis of the data to obtain the crack growth rate. Crack growth rates are then expressed as a function of crack tip intensity range Ak-, which is based on linear-elastic stress analysis. 

Make an elastic stress analysis of the product, which is an approximation. We calculate the maximum stress in the beam using Eq. (C.8) of Appendix C... 

The linear elastic stress analysis of a short fibre composite by the shear lag theory is due originally to H. L. Cox. The real composite (see Figure 6.32(a)) is assumed to deform in the vicinity of any particular fibre as if it were the model tem shown in Figure 6.32(b). In the model, the fibre (of diameter d) is surrounded 1 a cylinder of matrix of radius R, embedded in a homogeneous block of material which deforms as the composite as a... 

The problem of a crack meeting an interface in a composite as shown in Fig. 16.6(a) was posed by Cook and Gordon who wrongly concluded that the strength of the interface was important. Zak and Williams followed by Rice and Sih" also studied this problem using elastic stress analysis, but the problem was complicated mathematically and led to strange oscillating stresses near the crack... 

Elastic Stress Analysis and Equivalent Stresses. This is based off of the pre-2007 Section VIII, Division 2 methodology. Stress ranges will be the output values using this analysis. 

Elastic Stress Analysis - Simplified Elastic-Plastic Method. This method may be used in the case where the method indicated above shows the Pr + Pb + Q stress limits are not satisfied, but indicates that the Pl + Pb + Q range and excluding thermal effects must be less than Sps- Additionally, the effective alternating equivalent stress amplitude must include the fatigue penalty factor, ICej, which is based off of the simplified elastic-plastic criteria from the pre-2007 Section VIII, Division 2. Finally, a thermal stress ratcheting assessment must be made. 

Elastic Stress Analysis - Thermal Stress Ratcheting Assessment. This section will evaluate the allowable limit on the secondary stress range from cyclic thermal loading. 

The value of alternating stress taken from the fatigue curve is subject to other factors given hy the ASME Code. The ultimate allowable stress for a given number of cycles should be adjusted for these factors as follows (for elastic stress analysis and equivalent stresses ... 

The significance of is that it provides a measure of the magnitude of the stresses close to the tip of a sharp crack. Linear elastic stress analysis gives the following solution for the stresses acting at a point with polar coordinates r, 0 relative to the tip of such a crack in a wide sheet (see Fig. 5.19). 

The linear elastic stress analysis of a short fibre composite by the shear lag theory is due originally to H. L. Cox. The real composite (see Fig. 6.32(a)) is assumed to deform in the... 

Linear elastic stress analysis is then used to And stress and strain distributions and deflections, and the component is dimensioned so as to ensure that these all lie within allowable limits some iteration may be needed at... 

Bauschinger s effect. The ASME Code specifies some correction factors to be used in conjunction with elastic stress analysis that makes the evaluation plausible and in many cases conservative. 

There are two specific sections of the ASME Code that employ these correction factors. Both sections attempt to address the differences between the values by elastic computation and the real value, but have two distinct origins. The first one relates to the differences in volume between elastic and inelastic behaviors. NB 3227.6 of the ASME Code suggests using a modified Poisson s ratio, v, for elastic stress analysis as follows ... 

Stress divided by the modulus of the material results in the creep deformation. The deformation observed in a short-term tensile test at an elevated temperature is related to the deformation that takes place at a lower temperature over a longer period of time. The short-term data obtained can be used to obtain long-term modulus data through the development of a master modulus curve. Being able to determine the modulus at any time t and knowing the constant value of stress to which a material is subjected, it is possible to predict the creep which will have been experienced at time t by simply dividing the stress by the modulus using conventional elastic stress analysis relationships. 

In another approach, the deviation from Fickian diffusion is attributed to the dependence of the diffusion coefficient D on the volumetric strain c within the matrix. (Youssef et al. 2009). Employing an elastic stress analysis and reasonable assumptions regarding the equilibrium moisture content for the unstrained state, a time and space iterative scheme was developed to compute the coupling effects between strain and moisture uptake. 

If a linear elastic stress analysis is conducted to determine the stress distribution in the region surrounding a crack tip, it can be shown [21] that the stress state is given, with reference to Fig. 1, as ... 

The approximate elastic stress analysis of the remaining coating then gives the maximum interfacial shear stress, t, at crack initiation at the film-hole boundary ... 

With this linear elastic stress analysis, the correlation between crack initiation and stress distribution has been established. The interfacial cracking occurs at sites sustaining high peel stresses, while the bulk cracking results from the concentration of the equivalent stress. Thus, enhancing either the adhesion to the component or the bulk strength of the ICA joint will help to improve its reliability. 

There is the possibility to evaluate the results of an FE analysis based on Part 5 Design by analysis requirements. Part 5 describes the elastic stress analysis method, limit load analysis method, and the elastic-plastic stress analysis method. 

In EN 13445 Section 3 [8], there is the possibility to evaluate the results of an FE analysis based on Appendix C Procedure of stresses categories for the dimension based on analysis methods. Appendix C describes essentially the elastic stress analysis method. Stresses are determined using an elastic analysis, classified into categories, and limited to allowable values that have been conservatively estabUshed so that a plastic collapse will not occur. For thick-walled components, the plastic analysis methods in Appendix B Directly dimension with analysis methods are... 

In this constant-load-amplitude method, crack length is measured visually or by an equivalent method as a fimction of elapsed cycles, and these data are subjected to numerical analysis to establish die rate of crack growth. Crack growth rates are ttien expessed as a function of crack tip stress intensity range AAT, which is calculated from expressions basal on linear-elastic stress analysis. 

---