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<a href="/el" class="usa-nav__link">Engineering Laboratory</a>
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<a href="/itl" class="usa-nav__link">Information Technology Laboratory</a>
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<a href="/mml" class="usa-nav__link">Material Measurement Laboratory</a>
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<a href="/cnst" class="usa-nav__link">CNST NanoFab</a>
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<a href="/chips" class="usa-nav__link">CHIPS for America Initiative</a>
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<a href="/oam" class="usa-nav__link">Office of Advanced Manufacturing</a>
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<a href="/spo" class="usa-nav__link">Special Programs Office</a>
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<a href="/tpo" class="usa-nav__link">Technology Partnerships Office</a>
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<a href="/srm" class="usa-nav__link">Standard Reference Materials (SRMs)</a>
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<a href="/sri" class="usa-nav__link">Standard Reference Instruments (SRIs)</a>
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<a href="/standardsgov" class="usa-nav__link">Standards.gov</a>
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<a href="/pml/owm" class="usa-nav__link">Office of Weights and Measures</a>
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<p><span><span><span><span><span>Diffraction methods, regardless of the type of radiation used (election beam, X-ray, or neutrons) measure distances between ordered arrangements of atoms or, more precisely, between lattice planes in crystalline materials. Most materials are crystalline in structure; the differences are mostly in the size of the constituent crystals (also called grains). Interatomic distances change linearly with stress up to maximum values of several 10<sup>-3</sup> in relative terms at the so-called yield stress. Higher stresses cause plastic (permanent) deformation where, similar to spreading a deck of cards, slip occurs along atomic planes while the distance between planes stays the same. Continued slip often causes hardening and it increases the yield stress.</span></span></span></span></span></p>
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<img alt="stress measurement equation" height="288" loading="lazy" src="/sites/default/files/styles/480_x_480_limit/public/images/2023/02/15/Principles.jpg?itok=K2Iw6VDY" typeof="foaf:Image" width="385">
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<figcaption class="nist-image__caption">Interatomic distances are measured through Bragg’s equation which relates the wavelength of the radiation to the lattice spacing d. Constructive interference produces a diffraction peak whose centroid position determines the angle q. Credit: T.Gnaupel-Herold</figcaption>
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<p><span><span><span><span><span>Thermal neutrons have two key properties that enable the spatially resolved measurement of stress: 1) low absorption in most engineering materials allowing penetrations of several millimeters to centimeters, and 2) wavelengths </span></span><span><span><span>l</span></span></span><span><span> suitable for diffraction at angles at 2</span></span><span><span><span>q»</span></span></span><span><span>90</span></span><span><span><span>°</span></span></span><span><span> where spatial resolution is optimal.</span></span></span></span></span></p>
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<p><span><span><span><span><span>Aperture systems for the incident and diffracted neutron beams define the gage volume for which volume-averaged lattice spacings d are measured through Bragg’s law. The measured lattice spacing are subject to changes induced by stresses present at a given location in the sample. The orientation of the sample is critical for discerning the directionality of the stresses (stress tensor).</span></span></span></span></span></p>
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<p><span><span><span><span><span>During a measurement the neutron optical components remain unchanged; only the sample moves, either by translation or rotation. This way it is possible to accurately measure relative changes in d-spacings caused by stresses.</span></span></span></span></span></p>
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<img alt="spatially resolved stress measurement diagram" height="364" loading="lazy" src="/sites/default/files/styles/480_x_480_limit/public/images/2023/02/15/Princples2.jpg?itok=uGHDN5TH" typeof="foaf:Image" width="480">
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<figcaption class="nist-image__caption">Spatially resolved stress measurements. Credit: T. Gnaupel-Herold</figcaption>
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<p>Tri-axial stresses are determined from different locations in the sample and different orientations of the sample. Using the stress-free lattice spacing d<sub>0</sub> strains are obtained from which stresses are calculated through the generalized Hooke’s law. The value d<sub>0</sub> can be measured on small coupons or calculated from balance conditions.</p>
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<p><span><span><span><span><span>Strictly speaking, it is not necessary to define a gage volume for a measurement of applied stress if two conditions are met: a) stresses within the illuminated volume are homogeneous, and b) the sample remains stationary within the scattering plane. </span></span></span></span></span></p>
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