1.1 本试验方法涵盖了通过X射线衍射（XRD）实验测定准各向同性轴承钢材料宏观残余应力张量分量的程序。 1.2 该试验方法为通过实验确定应力值提供了指南，这些应力值在轴承寿命中起着重要作用。 1.3 如何使用张量值的示例有: 1.3.1 研磨类型和滥用研磨的检测； 1.3.2 车削操作中刀具磨损的测定； 1.3.3 渗碳和渗氮残余应力效应的监测； 1. 3.4 监测喷砂、喷丸和珩磨等表面处理的效果； 1.3.5 跟踪部件寿命和滚动接触疲劳效应； 1.3.6 故障分析； 1.3.7 残余应力松弛；和 1.3.8 可能影响轴承的其他残余应力相关问题。 1.4 单位- 以国际单位制表示的数值应视为标准值。本标准不包括其他计量单位。 1.5 本标准并非旨在解决与其使用相关的所有安全问题（如有）。本标准的用户有责任在使用前制定适当的安全、健康和环境实践，并确定监管限制的适用性。 1.6 本国际标准是根据世界贸易组织技术性贸易壁垒（TBT）委员会发布的《关于制定国际标准、指南和建议的原则的决定》中确立的国际公认标准化原则制定的。 ====意义和用途====== 5.1 本试验方法涵盖了通过XRD实验测定准各向同性轴承钢材料宏观残余应力张量分量的程序。此处，应力分量由张量σ表示 ij公司 如所示 等式1 ( 1. , 5. p、 40）。部件任何方向上的应力-应变关系由以下公式定义: 公式2 关于中定义的方位角φ（φ）和极角psi（ψ） 图1 ( 1. ，第132页）。 5.1.1 或者， 公式2 也可按以下布置显示( 2. ，第126页）: 5.2 利用XRD和布拉格定律，对多个方向进行了面间应变测量。方向的选择基于 公式2 ，这取决于所使用的模式。关于模式名称，文献中可能会发现相互冲突的术语。 例如，在欧洲可能被称为ψ（psi）衍射仪的东西在北美可能被称为χ（chi）衍射仪。这里考虑的三种模式将被称为ω、chi和修改chi，如中所述 9.5 . 5.3 欧米茄模式（Iso倾角）和Chi模式（侧倾角）- 沿一个φ方位角（设φ=0°）在多个ψ角处进行面间应变测量( 无花果。2和 3. )，减少 公式2 到 等式3 . 垂直于表面的应力（σ 33 )由于X的穿透深度较浅，因此假设不重要- 自由表面的射线，减少 等式3 到 等式4 . 测量后校正可用于解释可能的σ 33 影响( 12.12 ). 自σ ij公司 对于给定的方位角，值将保持不变 s 1. {hkl} 术语已重命名 C . 图2 σ测量的欧米茄模式图 11 方向 图3 σ测量的Chi模式图 11 方向 注1: 应力矩阵相对于表面法线旋转90° 图2 和 图14 . 5.3.1 测量的面间距值通过以下公式转换为应变: 等式24 , 等式25 或 等式26 . 等式4 用于拟合应变与sin 2. ψ产生σ值的数据 11 , τ 13 和 C . 然后可以对多个φ角（例如0、45和90°）重复测量，以确定全应力/应变张量。值σ 11 ，将影响数据的整体斜率，而τ 13 与椭圆开口的方向和程度有关。 图4 显示模拟 d 与罪恶 2. 所示张量的ψ剖面。这里的正20 MPaτ 13 应力导致椭圆开口，其中正psi范围向上打开，负psi范围向下打开。 较高的τ 13 值将导致较大的椭圆开口。负20 MPaτ 13 应力将导致相同的椭圆开口，只是方向相反，正psi范围向下打开，负psi范围向上打开，如所示 图5 . 图4 样品 d （2θ）与sin 2. 带σ的ψ数据集 11 =-500 MPa和τ 13 =+20兆帕 图5 样品 d （2θ）与sin 2. 带σ的ψ数据集 11 =-500 MPa和τ 13 =-20 MPa 5.4 修改的Chi模式- 面间应变测量是在多个β角上进行的，具有固定的χ偏移，χ m ( 图6 ). 不同β角的测量不能提供恒定的φ角( 图7 )因此， 公式2 不能以与ω和chi模式相同的方式进行简化。 图6 σ测量的修正Chi模式图 11 方向 图7 带χ的修正Chi模的ψ角和φ角与β角 m = 12° 5.4.1 公式2 应根据β和χ重写 m . 等式5和 6. 由直角球面三角形的解得出( 3. ). 5.4.2 将φ和ψ代入 公式2 具有 等式5和 6. （参见 X1.1 )，我们得到: 5.4.3 垂直于表面的应力（σ 33 )由于X射线在自由表面的穿透深度较浅，因此假设其不重要 公式7 到 等式8 . 测量后校正可用于解释可能的σ 33 影响（参见 12.12 ). 自σ ij公司 数值和χ m 在给定方位角下保持不变 s 1. {hkl} 术语已重命名 C ，和σ 22 术语已重命名 D . 5.4.4 σ 11 影响 d 与罪恶 2. β图类似于omega和chi模式( 图8 )但斜率应除以cos 2. χ m . 这增加了有效的 1. / 2. s 2. {hkl} 乘以1/cos 2. χ m 对于σ 11 . 图8 样品 d （2θ）与sin 2. 带σ的β数据集 11 =-500 MPa 5.4.5 τ ij公司 影响 d 与罪恶 2. β图更复杂，通常假设为零( 3. ). 然而，这可能不是真的，并且可能导致计算应力中的重大误差。 无花果。9- 13 显示 d 与罪恶 2. β考虑两个探测器位置时，单个剪切分量对修正chi模式的影响（χ m =+12°和χ m = -12°). 成分τ 12 和τ 13 在σ周围形成对称开口 11 任一探测器位置的斜率影响( 无花果。9- 11 ); 因此，σ 11 仍然可以通过简单地平均正负β数据来确定。将开口拟合到τ 12 和τ 13 虽然通过回归来区分这两种影响通常是不可能的，但术语可能是可能的。 图9 样品 d （2θ）与sin 2. 带χ的β数据集 m = +12°, σ 11 =-500 MPa和τ 12 =-100 MPa 图10 样品 d （2θ）与sin 2. 带χ的β数据集 m = -12°, σ 11 =-500 MPa和τ 12 =-100 MPa 图11 样品 d （2θ）与sin 2. 带χ的β数据集 m =+12或-12°，σ 11 =-500 MPa和τ 13 =-100 MPa 图12 样品 d （2θ）与sin 2. 带χ的β数据集 m = +12°, σ 11 =-500 MPa，τ 23 =-100 MPa，测量σ 11 =-472.5 MPa 图13 样品 d （2θ）与sin 2. 带χ的β数据集 m = -12°, σ 11 =-500 MPa，τ 23 =-100 MPa，测量σ 11 =-527.5 MPa 5.4.6 τ 23 值影响 d 与罪恶 2. β斜率与σ类似 11 对于每个探测器位置( 无花果。12和 13 ). 这是一个不必要的影响，因为σ 11 和τ 23 一个χ无法解决影响 m 位置在这种情况下，τ 23 -100 MPa的剪切应力导致计算的σ 11 χ的-472.5 MPa值 m =+12°或-527.5 MPa（对于χ） m =-12°，而实际值为-500 MPa。值σ 11 仍然可以通过平均两个χ的β数据来确定 m 位置。 5.4.7 可以使用修改的chi模式来确定σ 11 但应谨慎使用一个χ m 位置，因为可能存在τ 23 强调包括τ在内的多个剪切应力的组合 23 导致剪切影响越来越复杂。 由于这些原因，Chi和欧米茄模式优于改进的Chi。

1.1 This test method covers a procedure for experimentally determining macroscopic residual stress tensor components of quasi-isotropic bearing steel materials by X-ray diffraction (XRD). 1.2 This test method provides a guide for experimentally determining stress values, which play a significant role in bearing life. 1.3 Examples of how tensor values are used are: 1.3.1 Detection of grinding type and abusive grinding; 1.3.2 Determination of tool wear in turning operations; 1.3.3 Monitoring of carburizing and nitriding residual stress effects; 1.3.4 Monitoring effects of surface treatments such as sand blasting, shot peening, and honing; 1.3.5 Tracking of component life and rolling contact fatigue effects; 1.3.6 Failure analysis; 1.3.7 Relaxation of residual stress; and 1.3.8 Other residual-stress-related issues that potentially affect bearings. 1.4 Units— The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard. 1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. 1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee. ====== Significance And Use ====== 5.1 This test method covers a procedure for experimentally determining macroscopic residual stress tensor components of quasi-isotropic bearing steel materials by XRD. Here the stress components are represented by the tensor σ ij as shown in Eq 1 ( 1 , 5 p. 40). The stress strain relationship in any direction of a component is defined by Eq 2 with respect to the azimuth phi(φ) and polar angle psi(ψ) defined in Fig. 1 ( 1 , p. 132). 5.1.1 Alternatively, Eq 2 may also be shown in the following arrangement ( 2 , p. 126): 5.2 Using XRD and Bragg’s law, interplanar strain measurements are performed for multiple orientations. The orientations are selected based on a modified version of Eq 2 , which is dictated by the mode used. Conflicting nomenclature may be found in literature with regard to mode names. For example, what may be referred to as a ψ (psi) diffractometer in Europe may be called a χ (chi) diffractometer in North America. The three modes considered here will be referred to as omega, chi, and modified-chi as described in 9.5 . 5.3 Omega Mode (Iso Inclination) and Chi Mode (Side Inclination)— Interplanar strain measurements are performed at multiple ψ angles along one φ azimuth (let φ = 0°) ( Figs. 2 and 3 ), reducing Eq 2 to Eq 3 . Stress normal to the surface (σ 33 ) is assumed to be insignificant because of the shallow depth of penetration of X-rays at the free surface, reducing Eq 3 to Eq 4 . Post-measurement corrections may be applied to account for possible σ 33 influences ( 12.12 ). Since the σ ij values will remain constant for a given azimuth, the s 1 {hkl} term is renamed C . FIG. 2 Omega Mode Diagram for Measurement in σ 11 Direction FIG. 3 Chi Mode Diagram for Measurement in σ 11 Direction Note 1: Stress matrix is rotated 90° about the surface normal compared to Fig. 2 and Fig. 14 . 5.3.1 The measured interplanar spacing values are converted to strain using Eq 24 , Eq 25 , or Eq 26 . Eq 4 is used to fit the strain versus sin 2 ψ data yielding the values σ 11 , τ 13 , and C . The measurement can then be repeated for multiple phi angles (for example 0, 45, and 90°) to determine the full stress/strain tensor. The value, σ 11 , will influence the overall slope of the data, while τ 13 is related to the direction and degree of elliptical opening. Fig. 4 shows a simulated d versus sin 2 ψ profile for the tensor shown. Here the positive 20-MPa τ 13 stress results in an elliptical opening in which the positive psi range opens upward and the negative psi range opens downward. A higher τ 13 value will cause a larger elliptical opening. A negative 20-MPa τ 13 stress would result in the same elliptical opening only the direction would be reversed with the positive psi range opening downwards and the negative psi range opening upwards as shown in Fig. 5 . FIG. 4 Sample d (2θ) Versus sin 2 ψ Dataset with σ 11 = -500 MPa and τ 13 = +20 MPa FIG. 5 Sample d (2θ) Versus sin 2 ψ Dataset with σ 11 = -500 MPa and τ 13 = -20 MPa 5.4 Modified Chi Mode— Interplanar strain measurements are performed at multiple β angles with a fixed χ offset, χ m ( Fig. 6 ). Measurements at various β angles do not provide a constant φ angle ( Fig. 7 ), therefore, Eq 2 cannot be simplified in the same manner as for omega and chi mode. FIG. 6 Modified Chi Mode Diagram for Measurement in σ 11 Direction FIG. 7 ψ and φ Angles Versus β Angle for Modified Chi Mode with χ m = 12° 5.4.1 Eq 2 shall be rewritten in terms of β and χ m . Eq 5 and 6 are obtained from the solution for a right-angled spherical triangle ( 3 ). 5.4.2 Substituting φ and ψ in Eq 2 with Eq 5 and 6 (see X1.1 ), we get: 5.4.3 Stress normal to the surface (σ 33 ) is assumed to be insignificant because of the shallow depth of penetration of X-rays at the free surface reducing Eq 7 to Eq 8 . Post-measurement corrections may be applied to account for possible σ 33 influences (see 12.12 ). Since the σ ij values and χ m will remain constant for a given azimuth, the s 1 {hkl} term is renamed C , and the σ 22 term is renamed D . 5.4.4 The σ 11 influence on the d versus sin 2 β plot is similar to omega and chi mode ( Fig. 8 ) with the exception that the slope shall be divided by cos 2 χ m . This increases the effective 1 / 2 s 2 {hkl} by a factor of 1/cos 2 χ m for σ 11 . FIG. 8 Sample d (2θ) Versus sin 2 β Dataset with σ 11 = -500 MPa 5.4.5 The τ ij influences on the d versus sin 2 β plot are more complex and are often assumed to be zero ( 3 ). However, this may not be true and significant errors in the calculated stress may result. Figs. 9- 13 show the d versus sin 2 β influences of individual shear components for modified chi mode considering two detector positions (χ m = +12° and χ m = -12°). Components τ 12 and τ 13 cause a symmetrical opening about the σ 11 slope influence for either detector position ( Figs. 9- 11 ); therefore, σ 11 can still be determined by simply averaging the positive and negative β data. Fitting the opening to the τ 12 and τ 13 terms may be possible, although distinguishing between the two influences through regression is not normally possible. FIG. 9 Sample d (2θ) versus sin 2 β Dataset with χ m = +12°, σ 11 = -500 MPa, and τ 12 = -100 MPa FIG. 10 Sample d (2θ) Versus sin 2 β Dataset with χ m = -12°, σ 11 = -500 MPa, and τ 12 = -100 MPa FIG. 11 Sample d (2θ) Versus sin 2 β Dataset with χ m = +12 or -12°, σ 11 = -500 MPa, and τ 13 = -100 MPa FIG. 12 Sample d (2θ) Versus sin 2 β Dataset with χ m = +12°, σ 11 = -500 MPa, τ 23 = -100 MPa, and Measured σ 11 = -472.5 MPa FIG. 13 Sample d (2θ) Versus sin 2 β Dataset with χ m = -12°, σ 11 = -500 MPa, τ 23 = -100 MPa, and Measured σ 11 = -527.5 MPa 5.4.6 The τ 23 value affects the d versus sin 2 β slope in a similar fashion to σ 11 for each detector position ( Figs. 12 and 13 ). This is an unwanted effect since the σ 11 and τ 23 influence cannot be resolved for one χ m position. In this instance, the τ 23 shear stress of -100 MPa results in a calculated σ 11 value of -472.5 MPa for χ m = +12° or -527.5 MPa for χ m = -12°, while the actual value is -500 MPa. The value, σ 11 can still be determined by averaging the β data for both χ m positions. 5.4.7 The use of the modified chi mode may be used to determine σ 11 but shall be approached with caution using one χ m position because of the possible presence of a τ 23 stress. The combination of multiple shear stresses including τ 23 results in increasingly complex shear influences. Chi and omega mode are preferred over modified chi for these reasons.