Material Cost and Utilization
The material cost of a sheet metal part is based on rough mass required to make the part. The utilization is equal to the finish mass of the part divided by the rough mass—rough mass includes any material scrap.
The Material Selection dialog (in the Manufacturing Process pane) provides you with four options for calculating utilization:
• Rectangular Nesting: assumes the part is nested on a sheet based on its bounding box. In this case, the rough mass is equal to the total mass of the sheet divided by the number of parts nested on the sheet.
• True-Part Nesting: uses the component’s actual perimeter to determine nesting, and tests various rotations of the component. See User Inputs for information on Step Angle for True-Part Shape Nesting. True-part nesting is the default utilization method for baseline VPEs (but see the plant variable defaultUtilizationMethod), since it usually results in closer nesting, yielding higher material utilization.
• Machine Default: uses the current machine’s associated average material utilization (the machine property Avg Utilization); use this to estimate material costs for dynamic nesting.
• Override: uses a fixed utilization value entered by user; use this when you know the exact utilization based on a supplier’s nesting pattern.
The current nesting pattern on the currently selected stock is viewable in the Viewer using the Analysis menu. The stock can be changed via the Material Selection dialog.
You can display the flat pattern head on, in a separate window, together with its associated SER, by selecting Flat Outline from the Analysis menu in the Viewer toolbar.
Flattening
aPriori provides two alternative methods for determining the outline of the flattened part, finite element analysis (FEA)-based flattening and geometric flattening:
• FEA flattening:
o Analysis is based on a forming simulation which uses a finite element analysis derived from the part’s CAD model and the properties of the selected material.
o More accurate than geometric flattening for formed and drawn automotive components and similar complex stampings.
o Generally slower than geometric flattening (very complex parts sometimes require more than one minute to flatten, although the great majority require far less time).
• Geometric flattening:
o Analysis is based on unfolding of CAD model geometry, and neither takes into account material properties nor simulates the forming process.
o Accurate for “mostly developable” parts, that is, parts consisting primarily of flat planar surfaces and simple bent or rolled surfaces, with a few small, isolated deformed features like gussets and stiffening beads. These types of parts are common in the agriculture/construction equipment and hi-tech industries.
o Generally faster than FEA flattening.
FEA flattening is used by default in starting point VPEs. VPE administrators can customize this default with the site variable flatteningSolverType.
For a given part, you can override the default flattening method, or configure FEA flattening, with the Flattening Options dialog, which is available from the Viewer toolbar.
The dialog provides the following options:
• Solver Type:
o FEA – Plastic and elastic material behaviors considered: takes into account both the elasticity-related material properties (including Young’s modulus and Poisson’s ratio) and the plasticity-related material properties (including K, the strain-hardening coefficient, N, the strain-hardening exponent, and R, the Lankford parameter, average) . This is the default in starting point VPEs.
o FEA – Only elastic behaviors considered: takes into account only the elasticity-related material properties (including Young’s modulus and Poisson’s ratio). Because only elastic behavior is modeled, blank size estimates are slightly larger with this option than with the “Plastic and elastic” option.  Some users prefer this approach as it is slightly more conservative for estimating material usage and costs.
o Geometric Unfolding: Select this if you don’t want to use FEA flattening.
The Flattening Method property of the Blank GCD indicates the method used for the most recent geometry extraction. It’s possible values are FEA_PLASTIC, FEA_ELASTIC, GEOMETRIC_UNFOLDING.
 
VPE administrators can customize the default solver type with the site variable flatteningSolverType.
• Surface for Flattening: applies to FEA flattening only. FEA flattening proceeds by imposing a mesh on an overall surface of the part. The mesh serves to divide the part into a large but finite number of discrete elements.
o Mid-Surface: specifies that the mesh should be imposed midway between one side of the part material and the other side of the part material. A mid-surface mesh basically represents the neutral surface of the part. This is the default in starting point VPEs.
o Larger Area Side: specifies that the mesh should be imposed on the larger-area side of the part material.
o Smaller Area Side: specifies that the mesh should be imposed on the smaller-area side of the part material.
VPE administrators can customize the default surface for flattening with the site variable flatteningSurface.
• Fill Holes in Blanks: applies to FEA flattening only.
o No: specifies that the mesh (see Surface for Flattening, above) should not be applied to portions of the material surface that will be removed to form a hole. This is the default in starting point VPEs.
o Yes: specifies that the mesh (see Surface for Flattening, above) should be applied to portions of the material surface that will be removed to form a hole.
VPE administrators can customize the default with the site variable flatteningFillHoleMethod.
• Flattening Direction: applies to FEA flattening only.
o aPriori Selected: specifies that the flattening calculation should be based on the ram direction chosen by aPriori. This option is available only in the Sheet Metal—Transfer Die process group, and is the default in starting point VPEs. See Ram Direction for Transfer Die for more information.
o Average Surface Normal: specifies that the flattening calculation should be based on a ram direction that is the average direction of the normal to the part’s surfaces. This is the only option available in the Sheet Metal process group.
VPE administrators for Sheet Metal—Transfer Die can customize the default flattening direction with the site variable flatteningDirection.
VPE Administrators also can customize the FEA flattening behavior with the following site variables:
• flatteningInitialStrainValue (0.002 in starting point VPEs): for FEA falttening, specifies the strain present in the material before outside forces and loads are applied.
• flatteningTimeoutSeconds (600 seconds in starting point VPEs): determines how long FEA flatteing will run before timing out; if FEA flattening times out or fails for any reason, an FEA-failure message appears in the Viewer, and geometric flattening is used instead. A value of 0 indicates no timeout—FEA flattening will run indefinitely.
As mentioned above, FEA flattening takes into account material properties, including the following:
• Young's Modulus
• Poisson's Ratio, K (strain-hardening coefficient)
• N (strain-hardening exponent)
• R (Lankford parameter, average). 
Materials in starting point VPEs specify these properties. If your VPE includes a material that doesn’t specify these properties, aPriori uses the following default values based on material type:
Material Type
Young's Modulus (MPa)
Poisson Ratio
K (strain-hardening coefficient, Mpa)
N (strain-hardening exponent, MPa)
R (Lankford parameter, average)
Aluminum
69000
0.33
341.1
0.21
0.7
Copper
115000
0.33
317
0.54
0.99
Galvanized Steel
207000
0.28
543
0.21
0.99
Stainless Steel
207000
0.28
1426
0.502
1
Steel
207000
0.28
0.28
479.3
1.345
 If the material type is not one listed in the table above, the entries for Steel are used.
True-part Nesting and Very Small Parts
True-part nesting usually uses both rectangular and grid nesting algorithms, but only grid nesting is used for parts that are very small compared to the sheet in which they are nested. Rectangular nesting, while it adds to nesting accuracy, can be very slow for such parts. VPE administrators can use the cost model variable highResolutionNestingFactor to adjust the threshold for identifying such parts and controlling which algorithms are used.
In starting point VPEs, highResolutionNestingFactor is set to 0.25, indicating that only grid nesting is used for parts whose surface area is less than one quarter of one percent of the area of the stock sheet. By decreasing this value, you can increase nesting accuracy, but you might also increase the amount of time required for the nesting calculations.
Formulas
Material Cost = Raw Material Cost – Scrap Material Credit – Scrap Part Credit
Material Cost depends on the following:
• Raw material cost: see formula
• Scrap material credit: this is 0 if the setup option Enable Scrap Material Credit is un-checked (the default in starting point VPEs). Otherwise, it is specified by the formula below.
• Scrap part credit: this is 0 if the setup option Enable Scrap Part Credit is un-checked (the default in starting point VPEs). Otherwise, it is specified by the formula below.
Raw Material Cost = (Material Cost Per Mass * Rough Mass) / Final Yield
Raw material cost is the cost of material for one part, including the cost of scrap produced during manufacture of the part, as well as the amortized cost of scrapped parts. It depends on the following:
• Material cost per mass: specified by the material property Cost per KG.
• Rough mass: see formula.
• Final yield: see Yields for Sheet Metal.
Rough Mass = Finish Mass / Utilization
Rough mass depends on the following:
• Finish mass: product of part Volume and material Density.
• Utilization: calculated by the cost engine. This is part mass divided by stock mass. See Material Cost and Utilization.
Utilization = Utilization Edge Scrap * Utilization Part Scrap
Utilization is the product of the following:
• Utilization edge scrap (see formula below)
• Utilization part scrap (see formula below)
Utilization Edge Scrap =
(Number of Parts Per Sheet * Blank Width * Blank Length) /
(Sheet Length * Sheet Width)
Utilization edge scrap is a function of the following:
• Number of parts per sheet (calculated based on part geometry, nesting type, and sheet dimensions)
• Blank width (obtained from GCD extraction)
• Blank length (obtained from GCD extraction)
• Sheet length (see the Material Stock section of the Material Selection dialog)
• Sheet width (see the Material Stock section of the Material Selection dialog)
Utilization Part Scrap =
Part Volume / (Blank Length * Blank Width * Part Thickness)
Utilization part scrap is a function of the following:
• Part volume (obtained from GCD extraction)
• Blank length (obtained from GCD extraction)
• Blank width (obtained from GCD extraction)
• Part thickness (obtained from GCD extraction)
Scrap Material Credit = Material Cost Per Mass * Scrap Cost Percent * Scrap Mass
Scrap material credit is the product of the following:
• Material cost per mass: specified by the material property Cost per KG.
• Scrap cost percent: this is 0 if the setup option Enable Scrap Material Credit is un-checked (the default in starting point VPEs). Otherwise, it is specified as a percentage by the material property Scrap Cost Percent.
• Scrap mass: see formula.
Scrap Mass = Rough Mass – Finish Mass
Scrap mass depends on the following:
• Rough mass: see formula.
• Finish mass: product of part Volume and material Density.
Scrap Part Credit =
(Material Cost per Kg * Scrap Cost Fraction) *
((Number of Scrap Parts + Number of Scrap Parts Down Stream) *
Rough Mass) /
Total Production Volume
Scrap part credit is 0 if the setup option Enable Scrap Part Credit is set to false. Otherwise, it is the product of the following:
• Material cost per mass: specified by the material property Cost per KG.
• Scrap cost fraction: this is 0 if the setup option Enable Scrap Part Credit is un-checked (the default in starting point VPEs). Otherwise, it is specified as a percentage by the material property Scrap Cost Percent.
• Number of scrap parts: number of parts discarded as scrap by this process. See Yields for Sheet Metal.
• Number of scrap parts down stream: number of parts discarded as scrap by downstream processes. See Yields for Sheet Metal.
• Rough mass: see formula.
• Total production volume: specified in the Production Scenario tab of the Cost Guide.