Loading stress

The computational process of analysis is hidden from the user, and visually the analysis is conducted in terms of M-02-91 or R6 [6] assessment procedure On the basis of data of stress state and defect configuration the necessary assessment parameters (limit load, stress intensity factor variation along the crack-like defect edge) are determined. Special attention is devoted to realization of sensitivity analysis. Effect of variations in calculated stress distribution and defect configuration are estimated by built-in way. 

Stress relaxation, while aUied to creep, is different (20—23). Stress relaxation is the time-dependent decrease in load (stress) at the contact displacement resulting from connector mating. Here, the initial elastic strain in the spring contact is replaced by time-dependent microplastic flow. Creep, on the other hand, relates to time-dependent geometry change (strain or displacement) under fixed load, which is a condition that does not apply to coimectors. 

At loading stresses between the HEL and the strong shock threshold, a two-wave structure is observed with an elastic precursor followed by a viscoplastic wave. The region between the two waves is in transition between the elastic and the viscoplastic states. The risetime of the trailing wave is strongly dependent on the loading stress amplitude [5]. 

L = loading stress S = material strength FS = faetor of safety. 

The distributional parameters for Kt in the form of the Normal distribution can then be used as a random variable product with the loading stress to determine the final stress acting due to the stress concentration. Equations 4.23 and 4.24 show... 

When dimensional variation is large, its effeets must be ineluded in the analysis of the stress distribution for a given situation. However, in some eases the effeets of dimensional variation on stress are negligible. A simplified approaeh to determine the likely stress distribution then beeomes available. Given that the mean load applied to the eomponent/assembly is known for a partieular situation, the loading stress ean be estimated by using the eoeffieient of variation, C, of the load and the mean value for the stress determined from the stress equation for the failure mode of eoneern. 

The load eoeffieient of variation Cv = 0.1. Rearranging the equation for to give the standard deviation of the loading stress yields ... 

Figure 4.24 A loading stress distribution with extreme events...

The theory is concerned with the problem of determining the probability of failure of a part which is subjected to a loading stress, L, and which has a strength, S. It is assumed that both L and S are random variables with known PDFs, represented by f S) and f L) (Disney et al., 1968). The probability of failure, and hence the reliability, can then be estimated as the area of interference between these stress and strength functions (Murty and Naikan, 1997). 

Addresses variability of loading stress and material strength... 

A meehanieal eomponent is eonsidered safe and reliable when the strength of the eomponent, S, exeeeds the value of loading stress, L, on it (Rao, 1992). When the loading stress exeeeds the strength, failure oeeurs, the reliability of the part, R, being related to this failure probability, P, by equation 4.26 ... 

It is also evident that the reliability ean also be derived by finding the probability of the loading stress being less than the strength of the eomponent ... 

This is demonstrated graphieally in Figure 4.27 whieh shows the loading stress remains less than some given value of allowable strength (Haugen, 1968 Rao, 1992). The probability of a strength in an interval dSi is ... 

Figure 4.27 SSI theory applied to the case where loading stress does not exceed strength...

When the loading stress ean be determined by a CDF in elosed form, this simplifies to ... 

Analytieal solutions to equation 4.32 for a single load applieation are available for eertain eombinations of distributions. These coupling equations (so ealled beeause they eouple the distributional terms for both loading stress and material strength) apply to two eommon eases. First, when both the stress and strength follow the Normal distribution (equation 4.38), and seeondly when stress and strength ean be eharaeterized by the Lognormal distribution (equation 4.39). 

Figure 4.28 Derivation of the coupling equation for the case when both loading stress and material strength are a Normal distribution...

Figure 4.30 Relative shape of loading stress and strength distributions for various loading roughnesses and arbitrary safety margin...

Gn L) is often difficult to determine for a given load distribution, but when is large, an approximation is given by the Maximum Extreme Value Type I distribution of the maximum extremes with a scale parameter, 0, and location parameter, v. When the initial loading stress distribution,/(L), is modelled by a Normal, Lognormal, 2-par-ameter Weibull or 3-parameter Weibull distribution, the extremal model parameters can be determined by the equations in Table 4.11. These equations include terms for the number of load applications, n. The extremal model for the loading stress can then be used in the SSI analysis to determine the reliability. 

For example, to determine the reliability, R , for independent load applications, we can use equation 4.33 when the loading stress is modelled using the Maximum Extreme Value Type I distribution, as for the above approach. The CDF for the... 

Table 4.11 Extremal value parameters from initial loading stress distributions...

The numerieal solution of equation 4.35 is suffieient in most eases to provide a reasonable answer for reliability with multiple load applieations for any eom bination of loading stress and strength distribution (Freudenthal et al., 1966). 

Consider the situation where the loading stress on a eomponent is given as Z, A (350,40) MPa relating to a Normal distribution with a mean of /i = 350 MPa and standard deviation cr = 40 MPa. The strength distribution of the eomponent is A (500, 50) MPa. It is required to find the reliability for these eonditions using eaeh approaeh above, given that the load will be applied 1000 times during a defined duty eyele. 

Maximum static loading stress, lmax> with variable strength... 

If we assume that the maximum stress applied is +3cr from the mean stress, where this loading stress value eovers 99.87% those applied in serviee ... 

Variable static loading stress with a defined duty cycle of n load applications with variable strength using approaches by Bury (1974), Carter (1997) and Freudenthal et al. (1966)... 

Next using Bury s approaeh, from Table 4.11 the extremal parameters, v and 0, from an initial Normal loading stress distribution are determined from ... 

Therefore, the loading stress CDF ean be represented by a 3-parameter Weibull distribution ... 

Figure 4.34 shows the reliability as a funetion of the number of load applieations, using the three approaehes deseribed to determine There is a large diserepaney between the reliability values ealeulated for n = 1000. Repeating the exereise for the same loading stress, A (350,40) MPa, but with a strength distribution of... 

The calculated loading stress, L, on a component is not only a function of applied load, but also the stress analysis technique used to find the stress, the geometry, and the failure theory used (Ullman, 1992). Using the variance equation, the parameters for the dimensional variation estimates and the applied load distribution, a statistical failure theory can then be formulated to determine the stress distribution, f L). This is then used in the SSI analysis to determine the probability of failure together with material strength distribution f S). 

Sy = yield strength Su = ultimate tensile strength L = loading stress Ty = shear yield strength. 

The shear stress, t, due to the assembly torque diminishes to zero with time, the preload, F, remaining constant, and so the stress on the solenoid section is only the direct stress,. v, as given in equation 4.75 (see Figure 4.41(b)) (Edwards and McKee, 1991). A second reliability can then be determined by considering the requirement that the pre-load stress remains above a minimum level to avoid loosening in service (0.5 S/)min from experiment) (Marbacher, 1999). The reliability, R, can then be determined from the probabilistic requirement, P, to avoid loosening ... 

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