METHOD FOR DETERMINING THE ELASTO-PLASTIC BEHAVIOR OF PARTS MADE OF AN ANISOTROPIC MATERIAL, AND USE OF SAID METHOD

摘要

A method of determining the elastoplastic behavior of components, in particular of gas turbine plants, at high temperatures. First of all, the linear-elastic behavior is determined and the inelastic behavior is taken into account on the basis of the linear-elastic results by using the Neuber rule, the anisotropic characteristics of the components, as occur in particular through the use of single-crystalline materials, are taken into account in a simple manner by using a modified anistropic Neuber rule in the form maths id="MATH-US-00001" num="00001" MATH OVERFLOW="SCROLL" MROW MSUP MIsigma/MI MROW MO*/MO MN2/MN /MROW /MSUP MO=/MO MROW MSUBSUP MIsigma/MI MIep/MI MN2/MN /MSUBSUP MO⁡/MO MROW MO(/MO MROW MN1/MN MO+/MO MROW MFRAC MROW MIA/MI MO⁢/MO MSTYLE mspace width="0.3em" height="0.3ex"/ /MSTYLE /MROW MIC/MI /MFRAC MO⁢/MO MFRAC MIalpha/MI MSUB MIE/MI MIR/MI /MSUB /MFRAC MO⁢/MO MSUP MROW MO(/MO MFRAC MROW MIA/MI MO⁢/MO MSTYLE mspace width="0.3em" height="0.3ex"/ /MSTYLE MO⁢/MO MSUBSUP MIsigma/MI MIep/MI MN2/MN /MSUBSUP /MROW MSUBSUP MIsigma/MI MN0/MN MN2/MN /MSUBSUP /MFRAC MO)/MO /MROW MROW MIn/MI MO-/MO MN1/MN /MROW /MSUP /MROW /MROW MO)/MO /MROW /MROW /MROW /MATH /MATHS where A=inelastic anisotropic correction term, maths id="MATH-US-00002" num="00002" MATH OVERFLOW="SCROLL" MTABLE MTR MTD MROW MIA/MI MO=/MO MI/ MO⁢/MO MROW MFRAC MN1/MN MN2/MN /MFRAC MO[/MO MROW MSUP MROW MIF/MI MO⁡/MO MROW MO(/MO MROW MSUB MID/MI MIyy/MI /MSUB MO-/MO MSUB MID/MI MIzz/MI /MSUB /MROW MO)/MO /MROW /MROW MN2/MN /MSUP MO+/MO MSUP MROW MIG/MI MO⁡/MO MROW MO(/MO MROW MSUB MID/MI MIzz/MI /MSUB MO-/MO MSUB MID/MI MIxx/MI /MSUB /MROW MO)/MO /MROW /MROW MN2/MN /MSUP MO+/MO /MROW /MROW /MROW /MTD /MTR MTR MTD MROW MI/ MO⁢/MO MROW MROW MIH/MI MO⁢/MO MSUP MROW MO(/MO MROW MSUB MID/MI MIxx/MI /MSUB MO-/MO MSUB MID/MI MIyy/MI /MSUB /MROW MO)/MO /MROW MN2/MN /MSUP /MROW MO+/MO MROW MN2/MN MO⁢/MO MIL/MI MO⁢/MO MSTYLE mspace width="0.3em" height="0.3ex"/ /MSTYLE MO⁢/MO MSUBSUP MID/MI MIyz/MI MN2/MN /MSUBSUP /MROW MO+/MO MROW MN2/MN MO⁢/MO MSTYLE mspace width="0.3em" height="0.3ex"/ /MSTYLE MO⁢/MO MSUBSUP MIMD/MI MROW MIz/MI MO⁢/MO MSTYLE mspace width="0.3em" height="0.3ex"/ /MSTYLE MO⁢/MO MIx/MI /MROW MN2/MN /MSUBSUP /MROW MO+/MO MROW MN2/MN MO⁢/MO MSTYLE mspace width="0.3em" height="0.3ex"/ /MSTYLE MO⁢/MO MSUBSUP MIND/MI MROW MIx/MI MO⁢/MO MSTYLE mspace width="0.3em" height="0.3ex"/ /MSTYLE MO⁢/MO MIy/MI /MROW MN2/MN /MSUBSUP /MROW /MROW MO]/MO /MROW /MTD /MTR /MTABLE /MATH /MATHS where F, G, H, L, M and N are the Hill constants, C=elastic anisotropic correction term, C=U STYLE="SINGLE"D.U STYLE="DOUBLE"ESUP-1/SUP.U STYLE="SINGLE"D U STYLE="SINGLE"sigma*=determined linear stress, U STYLE="SINGLE"sigmaSUBep/SUB=estimated inelastic stress, U STYLE="SINGLE"D=direction vector of the elastic and inelastic stresses U STYLE="DOUBLE"ESUP-1/SUP=inverse stiffness matrix, ESUBR/SUB=reference stiffness, sigmaSUB0/SUB=reference stress, and sigma alpha, n=material constants.