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从入射线无负η倾角侧倾法X射线应力测定技术中的特殊几何关系出发,推导出其应力计算公式:2θ=asin~2ψ_0+bsinψ_0+c,σ_x=(Ksec~2η_0)a,τ_(xy)=(-Kcsc2η_0)b。在测出一组ψ_0角所对应的2θ值后,利用介绍的±ψ_0直线法或±ψ_0抛物线法,可以求出抛物线方程的系数a和b,从而求得测量方向上的正应力σ_x和σ_x作用面上的剪应力τ_(xy)。 误差分析结果表明:这种应力计算公式以及±ψ_0直线法和±ψ_0抛物线法两种测量计算方法,完全可以满足工程测量或实验室工作的要求。 由于入射线无负η倾角侧倾法一次测量可同时测得σ_x和τ_(xy),所以对试件表面上的一点只需要在二个方向上进行测量,就可确定其应力状态。 在入射线无负η倾角侧倾法测量中,如用常规法或入射线有倾角侧倾法应力计算公式计算应力,往往会产生较大的系统误差。系统误差的大小主要取决于测量方向上的正应力值及此正应力作用面上的剪应力值和η。 对入射线无负η倾角侧倾法应力计算公式和有关的分析,巳经用实验结果得到验证。

The stress calculation formulas for side inclination method without -η in-clining incident angle have been deduced based on its special geometrical rela-tions, the results obtained are as follow:2θ=αsin~2ψ_0+b sin ψ_0+c, σ_x= (K sec~2η_0)α, T_(xy)= (-K csc 2η_0)b After measuring a set of 2θ values corresponding to the incident angles ψ_0by this method, the coefficients α and b in the parabola equations can becalculated by ±ψ_0 linear method or ±ψ_0 Parabola method as presented in thetext, and normal stress σ_x in the measurement direction and shearing stressT_(xy) in the plane to which σ_x applied can thus be obtained. Results of erroranalysis show that the stress calculation formulas and the above ±ψ_0 methodscan satisfy requirements for either engineering or laboratory practice. As σ_2 and T_(xy) can be obtained simultaneously by a single measurement withthis method, so the state of stress at any point on the surface of the object canbe determined by measuring only in two directions at this point. If the 2θ values measured by side inclination method without -η incliningincident angle were treated by the stress calculation formulas of the convention-al method or the side inclination method with -η inclining incident angle, alarge systematic error may often be introduced, its magnitude being decidedmainly by the real values of σ_x, T_(xy) and η_0. The above derived stress calculation formulas are substantiated by experimentalresults.