Wolf Reinhardt

Calculation of Stress Intensity Factors for Cracks of Complex Geometry and Subjected to Arbitrary Nonlinear Stress Fields

Fatigue cracks in shot-peened and case-hardened notched machine components are subjected to stress fields induced by the external load and residual stresses resulting from the surface treatment. Both stress fields are characterized by nonuniform distributions, and handbook stress intensity factor solutions are in such cases unavailable, especially in the case of planar nonelliptical cracks. The method presented here is based on the generalized weight function technique enabling the stress intensity factors to be calculated for any Mode I loading applied to arbitrary planar convex and embedded crack. The stress intensity factor can be determined at any point on the crack contour by using one general weight function discussed in the paper. The weight function, m A , can be sufficiently well described by two quantities, i.e., the distance, p, from the load point, P(x, y), on the crack surface to the point, A, on the crack front where the stress intensity is to be calculated and the length, Γ c ., of the inverted crack contour. The stress intensity factors are calculated by integrating the product of the stress field and the weight function over the entire crack area. The general weight function and calculated stress intensity factors are validated against various numerical and analytical data. The numerical procedure for calculating stress intensity factors for arbitrary nonlinear stress distributions is briefly discussed as well. Several examples of typical input data and stress intensity factor results are presented including embedded and edge cracks subjected to two-dimensional stress fields. The method is particularly suitable for modeling fatigue crack growth in the presence of complex stress fields.

A Non-Cyclic Method for Plastic Shakedown Analysis

Shakedown is a cyclic phenomenon, and for its analysis it seems natural to employ a cyclic analysis method. Two problems are associated when this direct approach is used in finite element analysis. Firstly, the analysis typically needs to be stabilized over several cycles, and the analysis of each individual cycle may need a considerable amount of computing time. Secondly, even in cases where a stable cycle is known to exist, the finite element analysis can show a small continuing amount of strain accumulation. For elastic shakedown, non-cyclic analysis methods that use Melan’s theorem have been proposed. The present paper extends non-cyclic lower bound methods to the analysis of plastic shakedown. The proposed method is demonstrated with several example problems.Copyright

An efficient method for calculating multiaxial elasto-plastic notch tip strains and stresses under proportional loading

A method for calculating elasto-plastic notch tip strains and stresses in bodies subjected to proportional multiaxial loading is presented. Notch tip strains and stresses are estimated using the generalized Neubers rule and equivalent strain energy density method. These estimates form upper and lower bounds of the exact solution. All necessary relationships in the form of five simultaneous algebraic equations are derived for a general multiaxial stress state. An efficient solution method is proposed enabling fast calculation of numerical values and the choice of the appropriate solution. This method may be particularly useful for fatigue analysis of notched components.

The Elastic Modulus Adjustment Procedure (EMAP) for Shakedown

A simple and systematic procedure is proposed for shakedown analysis using combination of linear and non-linear finite element analysis (FEA). The method can identify the boundary between the shakedown and ratcheting domains directly does not require a time history analysis (non-cyclic). The proposed method is based on elastic modulus adjustment procedure (EMAP) and non-cyclic elastic-plastic FEA. The aim of EMAP is to generate statically admissible stress distributions and kinematically admissible strain distributions. By modifying the local elastic moduli it is possible to obtain an inelastic-like stress redistribution. The method is first demonstrated with a two-bar structure model based on analytical routine. The analysis is then applied to some typical shakedown problems including the “classical Bree problem” and the “bi-material cylinder”.Copyright

Strain Measures for Fatigue Assessment Using Elastic-Plastic FEA

In the ASME Code, Section III NB-3228.4(c) requires that if an elastic-plastic fatigue analysis is performed, the fatigue curve shall be entered with the numerically maximum principal total (elastic plus plastic) strain range multiplied by one-half the modulus of elasticity of the material at the mean cycle temperature. This paper discusses the choice of the principal strain range as well as other possible strain range measures for elastic-plastic fatigue analysis. Several generic observations that form the basis for the discussion are outlined.Copyright

On relating redistributed elastic and inelastic stress fields

The classical lower bound theorem in plasticity states that the load required to create equilibrium stresses in a structure that are below yield will always be less than or equal to the collapse load. Recent advances in determination of lower bound limit loads involve repeating elastic analyses after systematic modification of elastic moduli. The intention is to obtain lower bound limit loads from stress fields that would progressively approach a state similar to one at plastic limit. The gradual transformation of statically admissible stress fields from elastic to limit state can be compared to those corresponding to power-law creep indices, ranging from one to infinity. This paper attempts to investigate the possibility of establishing such relationships on a one-to-one basis, by considering standard component configurations.

Comparison of Cyclic and Burst Test Result With FE Simulation of a Locally Thinned Pipe Bend

Thinning of Carbon steel pipe subjected to water flow has been observed in many piping systems. The feeder pipes in CANDU® reactors have been found susceptible to this degradation mechanism. In response, an industry program has been initiated to investigate the effect of local thinning on structural integrity. A CANDU® feeder pipe bend specimen was thinned locally to about 70% of pressure based thickness near the weld at the onset of the bend. The test specimen was subjected to severe pressurized cyclic bending for over 1600 cycles, and was subsequently pressurized to failure under a constant applied bending deformation. The failed specimen was subjected to metallurgical examination. The present paper reports the results of a finite element analysis of the cyclic part of the test and an elastic plastic analysis for failure under pressurization. The results are compared with the experimental outcomes. The conclusions address specifically the test, more generally the failure of thinned pipe and the use of elastic-plastic finite element analysis to predict failure due to pressurization.Copyright

Investigation of the Elastic-Plastic Design Method in Section VIII Div. 2

Section VIII Div. 2 contains an elastic-plastic stress analysis option that is based on the ultimate instability load. The performance of the method is evaluated by using the PVRC burst disk tests. The prediction of the failure load is attempted using both a “best estimate” and the Section VIII Div. 2 material model. The strain limit against local failure is assessed as well. Starting from the notion that Design Codes try to establish safety margins against ultimate failure (burst) and against excessive deformation from the as-designed shape, this paper also examines the proposed method of using a factor of safety against instability (burst) in conjunction with a strain limit (protection against local failure). Implications for the application of the method to design are discussed.© 2009 ASME

On the Interaction of Thermal Membrane and Thermal Bending Stress in Shakedown Analysis

When the primary plus secondary stress range exceeds 3 Sm, the current ASME Code rules on simplified elastic-plastic analysis impose two separate requirements to evaluate the potential for ratcheting. The range of primary plus secondary stress excluding thermal bending must be less than 3 Sm, and the thermal stress must satisfy the Bree criterion for thermal stress ratchet. It has been shown previously that this method can be unconservative, i.e. predict shakedown when elastic-plastic analysis shows ratcheting. This paper clarifies the interaction between thermal membrane and bending stress in the presence of a primary membrane stress. An analytical model is used to derive the closed-form ratchet boundary for combined uniform loading of this type. The impact of having stress gradients along the wall that are typical for discontinuities is studied numerically. Simple modifications of the current Code methods are suggested that would achieve a clearer and better-justified set of rules.Copyright

Elastic-Plastic Shakedown Assessment of Piping Using a Non-Cyclic Method

The analysis for shakedown in nuclear Class 1 piping following NB-3600 of the ASME Boiler and Pressure Vessel Code contains several simplifications and can be overly conservative in some cases and potentially non-conservative in some others. A detailed elastic-plastic analysis following NB-3228.4, on the other hand, is computationally expensive and time consuming because an elastic-plastic model needs to be cycled to stabilization. A non-cyclic method to assess elastic plastic shakedown (absence of ratcheting) has been proposed and is applied to the analysis of some simple straight piping scenarios. Interaction diagrams similar to the Bree diagram are derived for other loading situations, such as thermal bending in conjunction with primary bending. The effect of piping boundary conditions on the ratchet boundary is explored.Copyright