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ASME STP-PT-080-2016 pdf download

1 GENERATION OF CREEP MODELS FOR 9CR-1MO-V STEEL (GRADE 91) ISOCHRONOUS CURVES 1.1 Introduction The intent of this report is to describe the development of a creep model for use in producing isochronous curves for grade 91. The basis for the other component of strain, the plasticity or “hot tensile” curve, has been described elsewhere. Values of creep strain are needed over a wide range of conditions. At some temperatures, stresses, and times, the creep strain is dominated by the primary component; at other conditions tertiary creep is important. The model must in some cases be predictive of conditions for which there are no available data, specifically estimating creep strains at very low stresses, high temperatures, and long times. In describing the model, we try to maintain a distinction between terms such as condition, parameter, constant, and coefficient. The conditions are the inputs to the model: stress, temperature, and time. The parameters of the model are the values that are used to describe the shape of the creep curve at a specific set of conditions. For example, the stress exponent, n, is a parameter, and the time to rupture, t r , may also be considered a parameter. The model coefficients are used in describing the parameters as functions of stress and temperature. The term constant is only used for specific coefficients that take on a special role in a time-temperature parameterization. In this report, the term constant is exclusively used for the Larson- Miller constant. It is highly desirable to keep the number of parameters low to minimize the effort of determining the coefficients. Many have come to view the classic three stage description of creep as the result of a primary stage where hardening mechanisms result in diminishing creep rates and a tertiary creep stage where damage and aging mechanisms produce an increasing creep rate. The second stage, where creep rate appears to be constant, is simply the transition between the two stages. Primary-tertiary forms for creep models often involve four parameters, two each for the primary and tertiary stages. To determine these parameters, three approaches are possible. The first is to fit the entire curve. This can be quite difficult depending on the creep model since it involves non-linear regression. The second is to fit either the tertiary creep or primary creep and then make adjustments for the missing component. The third is to fit each separately and look for a method to combine the curves. The model proposed below seeks to use information contained within the tertiary creep portion of the curve to provide an estimate of the primary creep strain.
This model has three parameters, K, A, and t r ; but rupture time has already been measured. Using the known time to rupture, Ellis fit the parameters, K and A, to all the actual creep curves using a least squares regression and then derived parametric expressions for each using the Dorn parametric fit. It is important to note that the constant, A, though conceptually the same in equations (1.9) and (1.22) are in practice different because they are determined in different ways. The A-parameter in equation (1.22) is affected by the primary creep term, and as such it does not necessarily produce the best possible fit to the tertiary portion of the curve. Ellis did not attempt to determine a separate fit to the primary portion of the curve, but if he had, it should be expected that the value of K would also be different. Non-linear combination model Both equations (1.8) and (1.22) represent linear combinations of primary and tertiary creep where the two creep strain functions do not interact. In the case of the Ellis approach, the whole curve is fit at once. In the case of the logarithmic rate model, the tertiary creep and primary creep parameters are derived separately.

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