34 2. RELAXATION TYPE RESIDUAL STRESS MEASUREMENT METHODS
hundred meters deep. On a smaller but still substantial scale, the Deep-Hole Method is also used
for measuring residual stresses in large metal castings at depths of several decimeters.
2.10 LAYER-REMOVAL METHOD
e Layer-Removal Method, schematically illustrated in Figure 2.9, is a long-established
method for measuring residual stresses in planar and cylindrical specimens. For planar spec-
imens, it involves measuring the deformation on one surface as layers of material are incre-
mentally removed from the opposite surface. e deformation measurements are typically done
using strain gauges or by optical measurements of surface displacements or curvature. For cylin-
drical specimens, deformation measurements are made on the outer surface as layers of material
are incrementally drilled from the center. Alternatively, for tubular specimens, measurements
can be made on the interior surface as layers of material are incrementally removed from the
outer surface. For cylindrical specimens, the Layer-Removal Method is commonly called Sachs’
Method.
(a) (b)
Strain Gauges
Layers to be
Removed
Layers to be
Removed
Strain Gauges
Figure 2.9: Layer-Removal Method. (a) Planar specimen and (b) cylindrical specimen (from
Schajer (2001)).
e Layer-Removal Method well exemplifies the action of the governing integral Equa-
tion (2.2). For example, for a tubular specimen, the relationship between the strains measured
on the interior surface as layers of material are incrementally removed from the outer surface is:
"
.r/ D
1
2
E
Z
r
a
2r
r
2
a
2
.R/ dR (2.3)
where
"
.r/ D "
.r/ C "
a
.r/ (2.4)
and where "
.r/ and "
a
.r/, respectively, are the circumferential and axial strains measured on
the interior surface when the radius of the outer surface is r, a is the radius of the inner measure-
ment surface, E is Young’s modulus and is Poisson’s ratio. e kernel function 2r=.r
2
a
2
/
corresponds to A.r; R/, where the original h and H in Equation (2.2) are here replaced by r and
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.