| ASTM E2860-20 - 1.11.2020 | ||||||||
| 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 ?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(?) and polar angle psi(?) 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 Braggs 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 ? (psi) diffractometer in Europe may be called a ? (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 ? angles along one ? azimuth (let ? = 0?) (Figs. 2 and 3), reducing Eq 2 to Eq 3. Stress normal to the surface (?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 ?33 influences (12.12). Since the ?ij values will remain constant for a given azimuth, the s1{hkl} term is renamed C. FIG. 2?Omega Mode Diagram for Measurement in ?11 Direction FIG. 3?Chi Mode Diagram for Measurement in ?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 sin2? data yielding the values ?11, ?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, ?11, will influence the overall slope of the data, while ?13 is related to the direction and degree of elliptical opening. Fig. 4 shows a simulated d versus sin2? profile for the tensor shown. Here the positive 20-MPa ?13 stress results in an elliptical opening in which the positive psi range opens upward and the negative psi range opens downward. A higher ?13 value will cause a larger elliptical opening. A negative 20-MPa ?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 (2?) Versus sin2? Dataset with ?11 = -500 MPa and ?13 = +20 MPa FIG. 5?Sample d (2?) Versus sin2? Dataset with ?11 = -500 MPa and ?13 = -20 MPa 5.4?Modified Chi ModeInterplanar strain measurements are performed at multiple ? angles with a fixed ? offset, ?m (Fig. 6). Measurements at various ? angles do not provide a constant ? 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 ?11 Direction FIG. 7?? and ? Angles Versus ? Angle for Modified Chi Mode with ?m = 12? 5.4.1?Eq 2 shall be rewritten in terms of ? and ?m. Eq 5 and 6 are obtained from the solution for a right-angled spherical triangle (3).
5.4.2?Substituting ? and ? in Eq 2 with Eq 5 and 6 (see X1.1), we get: 5.4.3?Stress normal to the surface (?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 ?33 influences (see 12.12). Since the ?ij values and ?m will remain constant for a given azimuth, the s1{hkl} term is renamed C, and the ?22 term is renamed D.
5.4.4?The ?11 influence on the d versus sin2? plot is similar to omega and chi mode (Fig. 8) with the exception that the slope shall be divided by cos2?m. This increases the effective 1/2?s2{hkl} by a factor of 1/cos2?m for ?11. FIG. 8?Sample d (2?) Versus sin2? Dataset with ?11 = -500 MPa 5.4.5?The ?ij influences on the d versus sin2? 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 sin2? influences of individual shear components for modified chi mode considering two detector positions (?m = +12? and ?m = -12?). Components ?12 and ?13 cause a symmetrical opening about the ?11 slope influence for either detector position (Figs. 9-11); therefore, ?11 can still be determined by simply averaging the positive and negative ? data. Fitting the opening to the ?12 and ?13 terms may be possible, although distinguishing between the two influences through regression is not normally possible. FIG. 9?Sample d (2?) versus sin2? Dataset with ?m = +12?, ?11 = -500 MPa, and ?12 = -100 MPa FIG. 10?Sample d (2?) Versus sin2? Dataset with ?m = -12?, ?11 = -500 MPa, and ?12 = -100 MPa FIG. 11?Sample d (2?) Versus sin2? Dataset with ?m = +12 or -12?, ?11 = -500 MPa, and ?13 = -100 MPa FIG. 12?Sample d (2?) Versus sin2? Dataset with ?m = +12?, ?11 = -500 MPa, ?23 = -100 MPa, and Measured ?11 = -472.5 MPa FIG. 13?Sample d (2?) Versus sin2? Dataset with ?m = -12?, ?11 = -500 MPa, ?23 = -100 MPa, and Measured ?11 = -527.5 MPa 5.4.6?The ?23 value affects the d versus sin2? slope in a similar fashion to ?11 for each detector position (Figs. 12 and 13). This is an unwanted effect since the ?11 and ?23 influence cannot be resolved for one ?m position. In this instance, the ?23 shear stress of -100 MPa results in a calculated ?11 value of -472.5 MPa for ?m = +12? or -527.5 MPa for ?m = -12?, while the actual value is -500 MPa. The value, ?11 can still be determined by averaging the ? data for both ?m positions. 5.4.7?The use of the modified chi mode may be used to determine ?11 but shall be approached with caution using one ?m position because of the possible presence of a ?23 stress. The combination of multiple shear stresses including ?23 results in increasingly complex shear influences. Chi and omega mode are preferred over modified chi for these reasons. | ||||||||
| 1. Scope | ||||||||
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?UnitsThe 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. | ||||||||
| 2. Referenced Documents | ||||||||
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