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Contour method

Hill Engineering measures residual stress with the contour method as part of our residual stress engineering practice and also on a fee-for-service basis for customers in the aviation, power generation, spacecraft, nuclear, and other industries.

Capabilities

The contour method for residual stress measurement is useful for quantifying the distribution bulk residual stress in three-dimensional parts. The method is capable of mapping a two-dimensional residual stress distribution across a plane through the 3D body. Contour can be applied successfully in a wide range of materials (metallic and some non-metallic) and part sizes (thickness range of 1 mm to 200+ mm).

The contour method is particularly useful for determining residual stress:

• Spatial distributions in 2D
  
• At significant depths from the surface (> 1 mm)
  
• In parts with large or complex geometry
  
• In surface treated parts (e.g., laser shock peened, roller burnished, carburized)
  
• In parts and materials with variable microstructure (e.g., welds)
  
• In parts and materials with large grain size

Measurement principle

According to the Theory of Elasticity, a body containing residual stress will deform as a result of sectioning, and the tractions required to restore the deformed part to its original shape are equivalent to the residual stress released by sectioning (as illustrated in the a-b-c sequence at right).

Through careful sectioning and precision inspection techniques it is possible to map complex 2D residual stress fields in a wide range of part geometries and materials. The contour method was invented circa 2000, patented by Los Alamos National Laboratory (USA), and was rapidly accepted and validated due to its unique capabilities. Through work at UC Davis, Hill Engineering personnel have been active in the development of contour and now, under license from Los Alamos, use the method to meet customer needs.

Experimental technique

A contour method measurement involves three primary steps: sectioning the part, measuring the distortion, and data analysis. The following is a brief summary of the experimental steps; additional detail on the measurement process is available (for example, these scholarly papers (one and two)).

Step 1 – Section the part

The first step of a contour method measurement is to section the part at the location where residual stress is to be measured. For metallic bodies, cutting is performed using a wire electric discharge machine (EDM). Wire EDM is used because it is a precise cutting method and has a minimal effect on residual stress in the body.

Step 2 – Measure the distortion

The second step of the contour method is to measure the deformation of the cut surfaces. This is accomplished using a precision scanning laser profilometer. The two halves of the part are placed on a measurement platform and distortion values are recorded over the entire surface.

Step 3 – Data analysis

The measured distortion data is converted to residual stress using a finite element based procedure. A finite element model of the part (after sectioning) is constructed. Next, a set of displacement boundary conditions are applied over the face of the finite element model corresponding to the location of the sectioning plane, where the displacement boundary conditions are computed as the average of the measured distortions from both halves of the sectioned part. Solving for equilibrium in the presence of the specified displacement boundary conditions provides the residual stress acting normal to the plane of the cut in the original part.