Design and Computational Analysis of Compound Castings and other Multi-Material Structures

This introductory paper is the research content of the paper ["Design and Computational Analysis of Compound Castings and other Multi-Material Structures"] published by ['Technische Universität Wien'].

1. Overview:

• Title: Design and Computational Analysis of Compound Castings and other Multi-Material Structures
• Author: Dipl.-Ing. Robert D. Bitsche
• Publication Year: April 2009
• Publishing Journal/Academic Society: Technische Universität Wien
• Keywords: compound casting, multi-material structures, quenching simulation, thermal contact conductance, finite element analysis, stress singularities.

2. Abstracts / Introduction

The multi-material lightweight design concept strives to use the “best” material and manufacturing process for each part of a structure in order to combine the advantages of different materials. Obviously, joining techniques play a major role in the manufac turing of these structures.

The compound casting process allows for the joining of a casting to other parts during the casting process. That is, the casting process serves both as a production and a joining process. The aim of this thesis is to develop computational methods for the analysis and design of compound castings and other multi-material structures. Both finite element methods and asymptotic analysis techniques are used.

During the quenching (or cooling) of a compound casting residual stresses develop due to the inhomogeneous transient temperature field and the dissimilar coefficients of thermal expansion of the materials involved. As these stresses determine the frictional connection and other important characteristics (e.g. the fatigue life) of the structure, the simulation of the quenching process is of central importance. In the case of purely contacting interfaces, i.e., if no metallurgical bonding exists, the heat transfer at the interface is either by contact or through the gap, and the thermal contact conductance at the bimaterial interface of the compound casting depends on contact pressure and gap opening.

A major finding of this thesis is that, in general, the consideration of this dependence is crucial to the simulation of the quenching process of compound castings. During the quenching process gaps can open up at the bimaterial interface even if the structure is geometrically simple. The opening of the gap severely reduces the thermal contact conductance and forces heat to flow mainly parallel to the open gap.

Practical examples of steel-aluminum compound castings with form-locking and/or frictional connection are presented. In general, the strength of these connections could be well predicted by the finite element simulations. Local stress concentrations can occur due to the abrupt change in material properties at the interface of a multi-material structure. Under the assumptions of linear elasticity theory, these stress concentrations can manifest themselves as stress singularities.

The dependence of the order of these singularities on geometrical and material parameters is examined in a systematic way and “design charts” are developed by which the order of the stress singularity can be directly registered. Using these charts, geometry modifications can be determined that either minimize the order of the stress singularity or lead to a regular stress field.

Often, great improvements can be achieved through comparatively small and local modifications of the geometry. Keywords: compound casting, multi-material structures, quenching simulation, ther mal contact conductance, finite element analysis, stress singularities.

3. Research Background:

Background of the Research Topic:

• The multi-material lightweight design concept aims to utilize the "best" material and manufacturing process for each structural component to maximize the benefits of diverse materials. Joining technologies are crucial in manufacturing these structures. Compound casting is a process that joins castings to other parts during the casting process itself, serving as both a production and joining method.

Status of Existing Research:

• Achieving a perfect, continuous metallurgical bond in industrial compound casting is challenging. Material-locking connections are often used alongside form-locking or frictional connections. However, cracks in brittle intermetallic layers can propagate along interfaces and deflect into adjacent materials, potentially reducing load-bearing capacity compared to purely form-locking or frictional connections.

Necessity of the Research:

• Residual stresses develop during the quenching of compound castings due to inhomogeneous temperature fields and differing thermal expansion coefficients. These stresses are critical as they influence the frictional connection and structural characteristics like fatigue life. Simulating the quenching process is therefore essential. Understanding and managing thermal contact conductance at bimaterial interfaces is also crucial for accurate quenching simulations, especially in the absence of metallurgical bonding.

4. Research Purpose and Research Questions:

Research Purpose:

• The primary aim of this thesis is to develop computational methods for analyzing and designing compound castings and multi-material structures. This involves employing both Finite Element Methods and asymptotic analysis techniques to address the complexities of these structures.

Key Research:

• Development of computational methods for analysis and design of compound castings.
• Investigation of residual stress development during quenching of compound castings.
• Analysis of thermal contact conductance at bimaterial interfaces during quenching.
• Examination of stress singularities at multi-material interfaces and development of "design charts".
• Application of finite element models for simulating quenching, machining, and mechanical testing of steel-aluminum compound castings.

5. Research Methodology

Research Design:

• This research employs computational methods, combining finite element analysis and asymptotic analysis techniques to investigate compound castings and multi-material structures.

Data Collection Method:

• The research relies on computational simulations using material properties and established theoretical models. Experimental data from mechanical testing of steel-aluminum compound castings are used for validation of the simulations.

Analysis Method:

• Finite Element Analysis (FEA): Used for simulating quenching, machining, and mechanical testing processes. Non-linear FEA is employed, considering thermo-elastic-plastic material behavior and thermal contact conductance.
• Asymptotic Analysis: Applied to investigate stress singularities at multi-material interfaces, developing analytical expressions and "design charts".

Research Subjects and Scope:

• Materials: Steel (S355, C45E) and Aluminum alloy (A356.0) compound castings.
• Processes: Quenching and heat treatment processes, machining operations, mechanical testing (tensile and push-out tests).
• Phenomena: Residual stress, thermal contact conductance, stress singularities, ductile failure.
• Geometries: Simple step-bars with axisymmetric inserts and a demo prototype of a compound casting.

6. Main Research Results:

Key Research Results:

• Thermal Contact Conductance: Consideration of variable thermal contact conductance, dependent on contact pressure and gap opening, is crucial for accurate quenching simulations of steel-aluminum compound castings without material-locking connections. Gaps at bimaterial interfaces significantly reduce thermal contact conductance, forcing heat to flow parallel to the gap.
• Stress Singularities: "Design charts" were developed to directly determine the order of stress singularities at multi-material interfaces based on geometrical and material parameters. These charts aid in geometry modifications to minimize stress singularities or achieve regular stress fields.
• Validation: Finite element simulations, incorporating variable thermal contact conductance and material models, effectively predicted the strength and failure modes of steel-aluminum compound castings in practical examples.

Analysis of presented data:

• Figure 2.2 illustrates the schematic dependence of heat transfer coefficient during quenching.
• Figure 2.6 shows the 0.2% proof stress of A356.0 in different tempers.
• Figure 3.2 shows the ratio of real to apparent contact area as a function of contact pressure.
• Figure 3.3 shows contact conductance due to conduction through actual contact spots.
• Figure 3.9 shows total thermal contact conductance at a steel-aluminum interface.
• Figure 6.6 illustrates temperature, radial stress and contact pressure during quenching simulation.
• Figure 6.8 compares measured and simulated force-displacement curves for push-out tests.
• Figure 7.9 shows circumferential residual stresses in the cast node after quenching and after removal of casting gate.
• Figure 7.10 shows Von Mises equivalent stress after removal of the casting gate.
• Figure 7.13 compares measured and simulated force-displacement curves for tensile tests.

Figure Name List:

• Figure 2.2: Schematic dependence of the heat transfer coefficient h on surface temperature ϑ during quenching
• Figure 2.6: 0.2% proof stress of A356.0 in different tempers.
• Figure 3.2: Ratio of the real to the apparent area of contact as a function of contact pressure for H = 600MPa.
• Figure 3.3: Contact conductance due to conduction through the actual contact spots hs as described by Equation (3.5) and the material properties and surface parameters in Table 3.1.
• Figure 3.9: Total thermal contact conductance at a steel-aluminum interface.
• Figure 6.6: Insert A: Temperature (Celsius), radial stress (MPa) and contact pressure t seconds after immersion into the quenching water
• Figure 6.8: Push-out test: Comparison of measured force-displacement curves (left column) to the ones obtained by simulation (middle column)
• Figure 7.9: Circumferential residual stresses in the cast node.
• Figure 7.10: Von Mises equivalent stress after removal of the casting gate depicted on an exploded view of the model.
• Figure 7.13: Tensile test.

7. Conclusion:

Summary of Key Findings:

• The research successfully developed computational methods for analyzing and designing compound castings, emphasizing the importance of considering variable thermal contact conductance in quenching simulations. Design charts for stress singularities were created, offering practical guidance for geometry optimization in multi-material structures. Finite element simulations were validated against experimental data, demonstrating their predictive capability for compound casting behavior.

Academic Significance of the Study:

• This study contributes to the fundamental understanding of heat transfer and stress development in compound castings. The developed "design charts" for stress singularities and methodologies for simulating thermal contact conductance offer valuable tools for academic research in multi-material design and analysis.

Practical Implications:

• The "design charts" provide practical guidelines for engineers to design compound castings with reduced stress concentrations, enhancing durability. The validated simulation methods enable optimization of casting processes and prediction of component performance, reducing prototyping costs and improving product reliability in industries utilizing compound casting technologies.

Limitations of the Study and Areas for Future Research:

• The study acknowledges limitations in material model complexity and the assumed constancy of certain parameters in thermal contact conductance models. Future research should focus on:
  • Experimentally verifying the thermal contact conductance model.
  • Determining static and kinetic coefficients of friction at steel-aluminum interfaces.
  • Developing more sophisticated material models, including elastic-visco-plastic constitutive models and models capturing the evolution of yield stress during natural ageing.
  • Experimentally determining fracture mechanics parameters for intermetallic phases in metallurgically bonded compound castings.

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9. Copyright:

• This material is "Robert D. Bitsche"'s paper: Based on "Design and Computational Analysis of Compound Castings and other Multi-Material Structures".
• Paper Source: http://www.ub.tuwien.ac.at/

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