CALCULATION OF DISTORTION AND RESIDUAL STRESSES OF CASTINGS THROUGH REMOVAL OF MATERIAL *

Prof. Dr.-Ing. H. Hoffmann,  Dipl.-Ing. T. Siggenauer,
Dipl.-Ing. T. Hanss,  Dipl.-Ing. St. Stanchev

Lehrstuhl fur Umformtechnik und Giessereiwesen, TU Munchen

Walther-Meissner-Strasse, 85747 Garching, Germany
tel.: 089/ 289-13791,  fax: 089/ 289-13738,   website: www.utg.mw.tum.de,   e-mail: sst@utg.mw.tum.de


1. Introduction and Short Description of the Research Project

By application of the current casting simulation systems it is possible to define the temperature fields in the mold and the cast parts quantitatively. Through the temperature field calculation the thermal induced stresses (first order) and the plastic displacements occurring in the material during the cooling process can be calculated. Before the machining proceeds, residual stresses occurring in the casting material are in the state of equilibrium. By the removal of material the state of equilibrium is destroyed on the functional surfaces and the cast part deforms until the state of equilibrium is reached again. This can lead, despite the previously accomplished quality control at the cast part, to the higher tolerance deviation and changed state of residual stresses in the finished part.

Fig.1. Closed CAE chain

The aim of the research is to close the CAE-chain between FEM strength analysis and the casting simulation in the development of cast parts, and to optimize the design of the cast part by the usual calculation effort. For this reason the deformation of the cast parts with the residual stresses should be calculated, while material is been removed during the processing of the raw part. The calculated state of stress and the deformation at the end of the manufacturing process of cast parts must be optimized in the strength analysis. Under consideration of component distortion by removal of material the cast parts' dimensional accuracy could be improved. The manufacturing tolerance can be controlled in the development phase, and the time necessary for product design can be shortened.


2. Development of a Mesh Independent Interface between SIMTEC and MARC/Mentat

Within the scope of this project a mesh independent interface between the casting simulation SIMTEC (RWP Ltd.) and FEM-program MARC/mentat (MSC) is developed. The principal function consists of the application of the resulting temperature distribution from SIMTEC as initial data in the program MARC/mentat, in order to calculate the residual stresses and later for strength analysis.

2.1. FE-Mesh and Postfile-Generation

In the analysis of the thermal casting processes the advantages of the simulation system SIMTEC are used. In the calculation of mechanical (static, dynamic) state of stress in the finished cast parts, the advantages of the simulation program MARC prevail. In order to use the advantages of both the programs, a separate calculation of thermal and mechanical stresses takes place in two different simulation systems. Thereby, first the thermal changes in the cast part are calculated with SIMTEC, and afterwards they are written in a post file. During a subsequently mechanical calculation in MARC the already calculated temperature fields are read from the post file and are applied as an initial boundary condition. This possibility is used for the interface between SIMTEC and MARC, whereby the temperature fields are calculated by SIMTEC, which is specially created for casting purposes. Later they are converted to a MARC post file. A direct transfer of the FE-mesh between both the programs is not possible because SIMTEC uses pentahedron elements, and MARC on the other side uses tetrahedron or hexahedron elements. In order to perform the stress calculation with the program MARC, the FE-meshes are created with the help of the program's specific methods. After carrying out the temperature field calculation with SIMTEC, there is a post file available. The file contains the information of the nodal coordinates and the corresponding temperatures depending on the time. A post file is also created with MARC. The MARC - and SIMTEC - post files are the base for the following conversion of the nodes from SIMTEC to the nodal coordinates in the FE-mesh from MARC.

2.2. Interpolation of the Nodal Temperatures and Calculation of Integration Points

Because the nodes and elements are not compatible, an interpolation of nodal temperatures and transfer from SIMTEC-mesh to MARC-mesh should take place. This is managed with the help of the program MeshTemp, which reads out the coordinates of the MARC-mesh from the MARC input file, interpolates the nodal temperatures from SIMTEC-mesh into the MARC-mesh and writes the data in a transfer file. The program MeshTemp is developed by the company RWP Ltd. in addition to the program SIMTEC. The main task is to transfer the calculated temperature fields into the nodes of the MARC-mesh.

Fig.2. Interpolation of nodal temperatures and
calculation of integration temperature points

The program SimMarc uses the transfer file, calculates the integration points for the MARC elements, and generates with the aid of the old MARC-post file a new MARC post file, which can be used for stress analysis. SimMarc has the task to generate a new post file from the interpolated nodal temperatures in the transfer file and from the old MARC-post file. The new generated post file contains the data from the SIMTEC temperature fields calculation, which are used further for the residual stress calculations. The individual steps for the transfer of temperature fields are presented in the following flow chart (Fig.3).

Fig.3. Transfer of temperature fields



3. Experimental Validation of the Interface

In order to compare the numerical values with the real thermotechnical and metal-cutting procedures, they must first be measured. Therefore extensive thermal measurements during and after casting, as well as residual stresses measurements of the sample geometry are necessary. In this way the results from the simulation will be checked and corrected.

3.1. Thermal Validation

3.1.1. Temperature Field Measurements of the Sample Geometry

The original sample geometry is a simple plate made of AlSi7Mg and is manufactured by gravity casting. The alloy AlSi7Mg corresponds to later used real cast parts. The casting device consists of one ground ingot mold made of hot working steel and a sand mold. By the use of a half ingot mold, a good heat removal from the cast part in one direction during the casting processes was possible. In the other direction a slowly cooling takes place because of the use of claybonded sand for the top part of the mold. In this way artificially different cooling velocities, good measurable deformation and residual stresses should be achieved. The sand mold simplifies the application of the case thermocouples in the mold cavity. Because the whole casting process, starting from the filling of the mold and finishing with the cooling at room temperature, must be technically covered, the thermocouples are to be cast into the plate. The thermocouples measure in 10 different points (Fig.4) with distance of 3 mm from the plate surface. The measurement takes place over the whole casting process while the part cools down. Additionally thermocouples are applied to the ground ingot mold, in order to follow the temperature progress in a distance of 3 mm from the contact surface between the ingot mold and the casting part.

Fig.4. System for
temperature field measurements


3.1.2. Simulation of Thermal Processes

The basis for generation of a finite-element-net for thermal calculation is a STL (standard transformation language)-file of the geometry. This STL-file is imported and meshed by the preprocessor of the simulation software. Fig.5 shows the FE-mesh of the sample geometry and a result from the temperature field calculation, whereby the gating system with sprue, runner, gate and riser and the holes for the thermocouples are implemented in the FE - model.

Fig.5. FE-model of the sample geometry
and a result from the thermal simulation

The time temperature cooling down curves of the measuring points (Fig.4) are compared with the results of the calculation. Fig.6 shows the comparison between the first simulation and the optimized simulation results. By the implementation of new material properties data for the thermal calculation (thermal conductivity, specific heat capacity, latent heat, density, liquid and solid temperature), the simulation results could be considerably improved.

Fig.6. Comparison between
thermal simulation and
measurements


3.2. Mechanical Validation

The dimensional variation of the casting plate in contrast to the target geometry was below the surface roughness. A distortion could not be proved by the measurements. This circumstance shows the relative low values of the residual stresses. Because no distortion was measurable in the sample geometry used at first, a new sample geometry was developed. The analysis shows that the cooling conditions of the part do not play a major role for the development of distortion, but the geometrical design does. Thereby, a sample geometry was used, which shows a visible distortion - a T-beam.

3.2.1. Residual Stresses and Distortion Simulation and Measurements of the Sample Geometry

The residual stresses in the cast samples are measured by using the hole-drilling method. The method is based on the interruption of the force equilibrium state by drilling a hole, which is so small, that the surface conditions of the part remains the same. For this purpose a drilling- and measuring system from the company SINT Technology, Florence, is used. The hole cancels the initial state of stress and a new state of equilibrium appears in the close surroundings. Thereby resulting spring back strains at the edge of the hole are measured with the previously introduced strain gauge with radial orientation. The strains measured are dependent on the depth of the hole. Therefore an evaluation of the stresses appearing on the surface of the part takes place via a calibration function, which includes the YOUNG`s modulus and the Poisson's ratio of the material. With these measurement techniques the depth dependent minimum and maximum main stresses and their direction can be determined. The measurement of the distortion was carried out with a 3D cordinate measuring machine. As data for the mechanical calculation, temperature dependent mechanical material properties from hot tensile tests (YOUNG`s modulus, yield strength, tensile strength) were determined and applied to the simulation. Additionally in the casting simulation the residual stresses and distortion are calculated. Fig.7 shows the deformed shape of the cast T-beam. There is one curve for the calculated distortion and one for the measured distortion. It is to be seen that the comparison analysis shows a good compliance between the distortion simulation and the measurements with the coordinate machine.

Fig.7. Comparison between stress simulation and measurements with the coordinate machine


3.2.2 Development of Simulation Methods for the Process Simulation

The simulation of the thermal process is fulfilled with the program SIMTEC. The residual stresses and strains during and after the casting process are calculated in MARC/Mentat or alternatively in SIMTEC. For the simulation of the removal of material in SIMTEC the corresponding areas of the FE-model as well as the forces acting on them are erased. A linear statical step of calculation delivers the node forces and displacements of the new state of equilibrium. In Fig.8 the result of the residual stress calculation of the T- beam and the created distortion based on the removal of material is shown.

Fig.8. Residual stresses variation
and new distortion by removal of material

For simulation of the removal of material in MARC/Mentat the calculated residual stresses- and strain values after the casting are applied as initial boundary condition for the further simulation of the stresses and strains from the metal-cutting process. The removal of material in the T- beam is qualitatively determined with the help of both simulation programs. The residual stress and distortion measurements after the metal-cutting operation are not yet considered. The distortion and the residual stresses in the end are calculated with MARC/Mentat. In this way, the real geometrical and thermo-mechanical properties of the final machined cast part are available for further strength analysis. In this way the results of the strength analysis could be optimized.


4. Literature
  1. N.N., Werkstoff-Datenblatt: G-AlSi7Mg; GK-AlSi7Mg; GF-AlSi7Mg, Aluminium Zentrale Dusseldorf 1998
  2. Honsel, Ch., Die Berechnung von Warme- und Eigenspannungen infolge von Abkuhlprozessen mit der Methode der tangentialen Steifigkeiten, Dissertation, Aachen 1992
  3. Kockelmann, H., The hole-drilling method - the best technique for the experimental determination of residual stresses in many fields of application, Messtechnischer Brief 29, MPA Stuttgart 1993
  4. Macherauch, E., Hauk, V., Eigenspannung. Entstehung-Messung-Bewertung. Band 1 und 2, Deutsche Gesellschaft fur Metallkunde e.V., 1985
  5. N. N., Datenbank des Simulationspakets SIMTEC, RWP GmbH, Roetgen 1997

* Paper of the 10th National Scientific-Technical Metalcasting Conference, October 3-4 2002, Lovech, Bulgaria