ASTM E2860-20

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.

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.

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 (σ₃₃) 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 σ₃₃ influences (12.12). Since the σ_ij values will remain constant for a given azimuth, the s₁^{hkl} term is renamed C.

FIG. 2 Omega Mode Diagram for Measurement in σ₁₁ Direction

FIG. 3 Chi Mode Diagram for Measurement in σ₁₁ 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 sin²ψ data yielding the values σ₁₁, τ₁₃, 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, σ₁₁, will influence the overall slope of the data, while τ₁₃ is related to the direction and degree of elliptical opening. Fig. 4 shows a simulated d versus sin²ψ profile for the tensor shown. Here the positive 20-MPa τ₁₃ stress results in an elliptical opening in which the positive psi range opens upward and the negative psi range opens downward. A higher τ₁₃ value will cause a larger elliptical opening. A negative 20-MPa τ₁₃ 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 sin²ψ Dataset with σ₁₁ = -500 MPa and τ₁₃ = +20 MPa

FIG. 5 Sample d (2θ) Versus sin²ψ Dataset with σ₁₁ = -500 MPa and τ₁₃ = -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