RATCHETING MODELS FOR FUSION COMPONENT DESIGN James P. Blanchard 1 , Carl J. Martin 1 , Mark Tillack 2 , and Xueren Wang 2 1 University of Wisconsin, Madison, WI, 53706, blanchard@engr.wisc.edu 2 University of California at San Diego, San Diego, CA, 92093, mtillack@ucsd.edu One of the primary failure mechanisms addressed by structural design rules for fusion components is ratcheting, the accumulation of strain with cyclic loads. If a component is loaded such that ratcheting occurs, failure can be expected in relatively short order, so design rules must ensure that the behavior is avoided. In this paper, we present finite element models for cyclic loading of typical fusion structures and compare the results to analytical models for simple geometries and design rules intended for more complex geometries. Both material and structural ratcheting is considered. For structural ratcheting, the 3Sm rule employed in the ITER Structural Design Criteria is found to be unduly conservative and the accompanying Bree rules are found, in some cases, to be non-conservative. Significant advantage can be gained from using fully plastic models to avoid ratcheting. I. INTRODUCTION One of the failure modes one must consider in designing a fusion component is ratcheting, which is an accumulation of strain with cyclic loadings. Shakedown occurs when the accumulation ceases and the strain saturates. Ratcheting cannot occur in a strain-controlled situation. There are two types of ratcheting. Material ratcheting occurs in the absence of structural effects, but only in some materials. It can occur in situations involving uniaxial stress which is uniform over a surface. Structural ratcheting can occur for any metal, but requires an inhomogeneous stress distribution. In this paper we will explore the ability of finite element codes to model ratcheting in fusion structures. We provide benchmark results for simple geometries experiencing both material and structural ratcheting. Having validated the commercial finite element code, we use it to explore several issues of interest to fusion designs. These issues include: the effect of using full stress strain curves, rather than perfectly plastic models; the effect of using design rules developed from simple cylindrical models to address ratcheting in other geometries, such as beams and typical fusion structures; and the degree of conservatism inherent in elastic design rules and elastic-plastic design rules. II. MATERIAL RATCHETING As described earlier, material ratcheting is strain accumulation resulting purely from material effects. It can occur under conditions of uniform tensile stress and can be modeled using appropriate constitutive models that go beyond the typical stress-strain curve derived from a monotonic tensile test. It can be expected in several situations 1 : 1. In the case of an isotropically hardening material, ratcheting can occur if the strain increment under tension is not balanced by an equal compressive strain as the stress is cycled. 2. If a static mean stress is applied, if unloading does not completely offset the plastic strains developed during the initial load application 3. If the material properties are temperature dependent, rapid load changes can prevent material properties from responding instantaneously. 4. If the yield strength in tension differs from that in compression, then the direction of the strain vectors can differ between loading and unloading conditions, so they will not offset. 5. A similar effect occurs if the material is anisotropic. To model material ratcheting in a finite element code, one must employ a constitutive model that permits the phenomenon. The commercial code ANSYS includes a nonlinear kinematic hardening model called the Chaboche 2 model. The key feature of this model is a back stress term in the yield function. To test the ability of ANSYS to model material ratcheting, we ran a tensile test in an Alloy 4130 with a cyclic load ranging from -446 to 574 MPa. 3 The strain history for three different stress-strain curves is shown in Fig. 1. As can be seen in this figure, the strain saturates immediately for the typical kinematic and isotropic hardening curves, but for the Chaboche model, the plastic strain continues indefinitely as the cycles accumulate. This is evidence of material ratcheting. The Chaboche curve shows evidence of saturation, but running the FUSION SCIENCE AND TECHNOLOGY VOL. 60 JULY 2011 313