CHAPTER 2 LITERATURE STUDY
2.4 Residual Stress Determination
RS determination and prediction can take place in either destructive or non-destructive methods.
Destructive methods make use of strain measurements to determine and predict the RS within a component, whereas non-destructive methods predominantly make use of diffractive techniques for RS determination [7].
2.4.1 Contour Method
With regards to destructive distortion methods, a common approach used to measure bulk RS is known as the contour method. With application of the contour method, the static equilibrium boundary condition of the RS in the component is exploited. Consequently, upon cutting the component using wire electron discharge machining (EDM), static equilibrium of the cut face is re-defined through deformation [66],[67]. This deformation is then measured by means of a coordinate measurement machine or similar suitable three-dimensional measurement apparatus [66].
The coordinates generated from the measurement technique are defined in a finite element environment, whereupon the stress required to cause the face to deform to its original flat surface is the assumed elastic RS within the component prior to the loss of the cutting procedure [66].
Ahmad et al. found that using the contour method correlated well with numerically simulated RS within a component, however variation was observed when analysing near surface RS with this experimental method (less than 1 mm from surface) [34]. This is further corroborated by Prime et al. noting that the contour method is more suited for interior determination of RS magnitude and distribution than for surface or near surface RS [66]. A further short-coming of this method is the inability to derive the triaxial RS state, only able to calculate the RS normal to the cut face.
2.4.2 Inherent Strain Method
The ISM is a finite element solution method capable of RS prediction in AM components.
Proposed by Ueda in 1985, the initial usage of the ISM was to determine the state of stress within welded regions of components, applied by sectioning the component and measuring the eigenstrain, known commonly as inherent strains, at specified locations [68]. From this a spatially varying inherent strain field may then be applied to derive the RS in both sectioned and un- sectioned areas within the weld bead [69],[70]. This method of RS determination has since been adapted for usage in predicting RS within AM processes.
In order to accurately and expediently estimate the RS within a component, the ISM has seen some modification to create macroscopic solution types which are able to simulate at a component scale; the more accurate micro-scale simulations coming at too great a computational cost [71]. As the individual layer sizes during manufacturing of the component are in the order of 20-100 µm, layers are bulked together to create an element layered equivalent representing the combined layers [7]. This bulked layer then generally employs hexahedral elements to create a flat-topped surface using the element birth approach [34],[52],[71],[72]. Research has also shown that mesh coarsening during mechanical or thermomechanical simulations of the AM process
may reduce run times by a factor of 10, while maintaining distortion prediction within 10% of experimentally measured values [52],[72],[73].
The SLM process is then simulated through the elemental layer by layer addition of the surface area into the FEM model. This addition of the element layer is given a strain tensor for each of the elements, as shown in Figure 2-9, for a two-dimensional problem.
The strain tensors used in the macro-scale simulation of the component may be derived from single layer micro-scale simulations with moving heat input source on the layer, or purely macroscopically through the measurement of the deformation of a cantilever specimen [53],[74],[75]. The solution of the model then yields the state of stress due to the addition of this layer, with the process being repeated until all layers have been added. For this layer-by-layer approach to the simulation, mechanical and thermomechanical approaches have been used [37],[52],[55],[71],[72].
Elements before addition of strain tensor.
Element deformation with application of strain.
Newly added elements (element birth).
Elements with addition of strain tensor.
Єxx
Figure 2-9: Element birth on a single layer with the application of an inherent strain tensor.
For the mechanical and thermomechanical simulation types, experimental calibration of the inherent strains of the elements may be done through deformation measurements of cantilever type specimens. Multiple sources in the literature use a cantilever specimen with geometry similar to that shown in Figure 2-10, with the deflection of the cantilever upon cutting on the red dotted line used to determine strain values over the elements and then determining an inherent strain or volumetric expansion for the process parameters used in cantilever production [64],[74],[75].
Limitations of the ISM may however be present as the geometry of the calibration component may result in inaccurate inherent strain values especially when the top thickness of the component is less than 2 mm [71].
The mechanical ISM can be either isotropic or orthotropic, being able to solve for a single uniform strain tensor or two directional strain tensors respectively. The strain tensors derived from the interpolated values of the cantilever specimens are then used in the simulation of a component with each layer of elements assigned strain values. In order to calibrate the isotropic ISM a single cantilever specimen is required while the orthotropic type calibrations use two cantilevers, with scanning vectors perpendicular to one another, thereby calculating different inherent strains for both the X and Y directions [76],[77].
For the thermomechanically coupled ISM, a similar isotropic solution is used. These simulations use a volumetric expansion factor for the elements of a layer in a coupled thermal-mechanical finite element model. A layer’s heat input is simulated in a thermal model to determine the temperature field of the elements with the subsequent mechanical analysis deriving the resultant RS as a result of the newly added layer [37],[77]. By calculating the strain resulting in cantilever deformation, element volumetric expansion is calibrated for a specific set of process parameters for use in the thermomechanical ISM.
The ISM is shown to provide good agreement for distortion prediction however with less accurate RS prediction [73]. The ISM may result in some inaccuracies, namely discrepancies between the macro-scale ISM and experimentally measured values for stress. The differences may arise from
Deflection measurement
point
Figure 2-10: Calibration cantilever geometry.
the dependency of the strain on the geometry of the calibration samples as well as potential thermal interactions due to the placement of multiple parts on a single build plate [71]. Thus, for larger build plates it would be necessary to incorporate a spatially varying field for the inherent strains on the build plate [77].
2.4.3 Diffractive Techniques
These methods are based on the usage of Bragg’s law of diffraction; where X-rays or neutrons are directed onto a specified volume (explanation in section 3.4). Diffraction occurs, allowing for the measurement of the distance between crystal lattice planes [78]. Through comparison of the interplanar distances between a stressed and unstressed reference specimen, the strains and stresses may be derived [78]. X-ray diffraction has been used to determine the RS of IN718 SLM specimens, however due to low penetration depths, this method is limited to only a few microns beneath the surface of a specimen [59].
ND is similar to X-ray diffraction with respect to the application of Braggs law to determine crystal lattice spacing. Having greater penetrations depths than X-rays, ND is capable of determining the RS within the bulk of a sample, helping observe the RS formation as a result of various process parameters [79]. Accordingly, ND has been used for validation of results from destructive measurements [66],[80]. This method has also been used to determine RS values of thin and thick-walled specimens and large structures of varying geometry for metallic AM components [79],[80]-[82]. The ND technique does have limitations which include, minimum measurement depth from surface of the specimen, and sensitivity to microstructural variations within the component [34],[79]. ND has been successfully used to measure RS in IN718 SLM components.
RS correlating to scanning strategy, component build orientation, geometric features, thinning of the build plate and removal from the build plate have been investigated for IN718 and used to verify simulation results [79],[83]-[85].