Finite Element Analysis of Interfacial Debonding in Copper/Diamond Composites for Thermal Management Applications

At a Glance

Metadata	Details
Publication Date	2017-07-02
Journal	Materials
Authors	Muhammad Zain-ul-abdein, Hassan Ijaz, Waqas Saleem, Kabeer Raza, Abdullah S. Bin Mahfouz
Institutions	University of Jeddah, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology
Citations	12
Analysis	Full AI Review Included

Technical Analysis of Copper/Diamond Composites for High-Performance Thermal Management

6CCVD Material Analysis & Application Brief

Executive Summary

This analysis focuses on the Finite Element Analysis (FEA) of Copper/Diamond (Cu/D) composites, critical for high-heat flux thermal management applications (e.g., heat sinks). The core challenge addressed is interfacial debonding caused by the extreme mismatch in the Coefficient of Thermal Expansion (CTE) between Copper (~16.7 x 10^-6 K^-1) and Diamond (~0.89 x 10^-6 K^-1).

Category	Summary Point
Primary Challenge	High thermal stresses in the Cu matrix adjacent to the diamond interface lead to plastic deformation and subsequent debonding under thermal loading.
Material Solution	Utilizing an intermediate coating material, specifically Chromium (Cr) in this study (CTE ~6.1 x 10^-6 K^-1), significantly mitigates stress localization.
Quantified Achievement	Cr-coated diamond reduced the maximum interfacial separation (debonding) by approximately 45% (from 21.3 µm down to 11.8 µm) compared to uncoated diamond under steady-state thermal loading.
Modeling Insight	A fully coupled thermo-mechanical FEA using micro-scale SEM data revealed that cyclic thermal loading (transient analysis) induces significantly higher peak Mises stresses (up to 300 MPa at 160 °C) compared to steady-state loading, increasing thermal fatigue risk.
Application Relevance	The computational methodology successfully predicts service life degradation by correlating CTE mismatch, interfacial bond strength (cohesive behavior), and stress localization.
6CCVD Value	6CCVD supplies the high-purity Single Crystal (SCD) and Polycrystalline (PCD) diamond required for these composite fillers and provides custom interfacial coating services (Ti, W, Pt, Au, Pd, Cu) and engineering support to optimize bond strength and conductive properties.

Technical Specifications

The following hard data points were extracted from the FEA modeling and material property definitions, demonstrating the operating environment and material responses.

Parameter	Value	Unit	Context
Diamond Thermal Conductivity (TC)	2000	W·K^-1·m^-1	Ideal high-performance filler material.
Copper Thermal Conductivity (TC)	~400	W·K^-1·m^-1	Matrix material baseline.
Diamond CTE	~0.89 x 10^-6	K^-1	Low expansion coefficient (primary cause of mismatch).
Copper CTE	~16.7 x 10^-6	K^-1	High expansion coefficient.
Chromium (Cr) CTE	~6.1 x 10^-6	K^-1	Intermediate layer chosen to reduce mismatch.
Yield Strength (Copper, σ_y)	90	MPa	Yield stress threshold at 0 plastic strain (T=T₀).
Max Interfacial Separation (Uncoated D)	21.3	µm	Debonding gap under steady-state loading (Case 2).
Max Interfacial Separation (Cr-Coated D)	11.8	µm	Debonding gap under steady-state loading (Case 3).
Maximum Operating Temperature (Transient)	160	°C	Peak temperature for cyclic thermal fatigue analysis (T_max).
Peak Mises Stress (Transient, 160 °C)	300	MPa	Maximum stress observed in Cu matrix under cyclic heating.
Diamond Volume Fraction	20	vol %	Microstructure selected for maximum matrix discontinuity/stress analysis.
Cr Coating Thickness	0.3 - 1	µm	Diffusion method coating thickness used in composite fabrication.

Key Methodologies

The study employed a combination of powder metallurgy fabrication and advanced micro-scale Finite Element Analysis (FEA) to simulate thermal fatigue and interfacial failure.

Composite Fabrication:
- Method: Powder metallurgy and conventional sintering in a vacuum tube furnace.
- Matrix: Irregular Copper (Cu) powders (45 µm particle size).
- Filler: Cubo-octahedral shaped diamonds (100 µm particle size).
- Coating: Cr coating applied via diffusion method, resulting in a thickness range of 0.3 µm to 1 µm.
FEA Model Generation:
- Input Geometry: 2D micrograph derived from SEM images of the Cu/20 vol % diamond composite.
- Software: Abaqus/Standard (v6.16).
- Coupling: Fully coupled thermo-mechanical analysis (simultaneous calculation of temperature and mechanical response, accounting for plastic energy dissipation).
- Element Types: CPE4RT (4-node bilinear coupled temperature-displacement plane strain quadrilateral) and CPE3T (3-node linear coupled triangular).
Boundary Conditions (BCs) and Loading:
- Steady-State (PL - Parallel Orientation): Temperature gradient applied: T_OP = 100 °C (Source) to T_QR = 20 °C (Ambient).
- Transient (PD - Perpendicular Orientation): Cyclic loading applied to all nodes: T_max = 100 °C up to 160 °C; Temperature rate = 100 °C/s.
- Interface Modeling:
  - Perfect Contact (Case 1 & 4): *TIE constraint, absolute thermal conductance.
  - Interacting Surfaces (Case 2 & 3): Mechanical contact defined by COHESIVE behavior (using maximum stress criteria) and thermal contact defined by finite conductance (14 kW·m^-2·K^-1).

6CCVD Solutions & Capabilities

This research confirms the critical role of material purity, particle morphology, and interface engineering (coating) in manufacturing reliable diamond-metal matrix composites for thermal management. 6CCVD’s expertise in MPCVD diamond production and custom thin-film deposition directly supports the replication and advancement of this research.

Applicable Materials

To replicate the high-purity diamond filler required for maximum thermal conductivity (TC > 2000 W·K^-1·m^-1) and consistent CTE, 6CCVD recommends the following base materials:

Optical Grade SCD Powder/Particles: For applications demanding ultra-high thermal conductivity diamond reinforcement derived from high-quality Single Crystal Diamond.
High Purity PCD Wafers/Plates (Custom Micronized): For bulk applications where uniform particle dispersion is critical, 6CCVD can process high-TC Polycrystalline Diamond into custom particle sizes (e.g., 100 µm diameter used in this study) with tight size distribution control.

Interface Engineering and Customization Potential

The study demonstrates that interface chemistry and intermediate CTE layers are essential for reducing thermal fatigue and preventing debonding. 6CCVD is an ideal partner for scaling this technology:

Research Requirement/Observation	6CCVD Specific Capability	Technical Advantage
Cr-Coating Requirement	While Cr is used in the study, 6CCVD offers extensive Metalization Services including Ti and W coatings, which literature (referenced in the paper) shows are also highly effective carbide formers for strong interfacial bonding.	Enables rapid material prototyping and testing of multiple interface layers with optimal carbide formation potential to further minimize CTE mismatch.
Thin Film Precision	The effective Cr layer thickness was 0.3 µm to 1 µm.	6CCVD offers in-house, controlled thin-film deposition down to sub-micron thicknesses (0.1 µm) across a range of metals (Au, Pt, Pd, Ti, W, Cu).
Thermal Cycling Resistance	Composites require robust bonding against extreme cyclic thermal stress (up to 300 MPa).	Our SCD and PCD materials exhibit superior mechanical integrity, and our custom metalization process ensures excellent adhesion and integrity of the interface layer, essential for thermal fatigue resistance.
Custom Dimensions	Although this paper focused on micro-scale particles, 6CCVD supplies plates/wafers up to 125mm (PCD) and substrates up to 10mm thick, suitable for large-scale heat spreader fabrication or next-generation composite targets.	Allows engineers to transition seamlessly from micro-scale FEA validation to macro-scale component manufacturing.

Engineering Support

The complexity of fully coupled thermo-mechanical analysis (as used in Cases 3 and 4) requires deep material and process knowledge. 6CCVD’s in-house PhD engineering team specializes in diamond material behavior, thermal conductivity modeling, and interfacial stress management.

We can assist customers in:

Selecting the optimal diamond grade (SCD vs. PCD) and particle morphology (cubo-octahedral/custom shapes).
Designing interface metalization strategies (e.g., Ti/Pt/Au stacks) to achieve desired cohesive strength and thermal boundary conductance for specific High-Power Microelectronic Thermal Management projects.
Consulting on sintering parameters and CTE matching to predict and mitigate thermal fatigue failure, thereby increasing the service life of finished components.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Copper/diamond (Cu/D) composites are famous in thermal management applications for their high thermal conductivity values. They, however, offer some interface related problems like high thermal boundary resistance and excessive debonding. This paper investigates interfacial debonding in Cu/D composites subjected to steady-state and transient thermal cyclic loading. A micro-scale finite element (FE) model was developed from a SEM image of the Cu/20 vol % D composite sample. Several test cases were assumed with respect to the direction of heat flow and the boundary interactions between Cu/uncoated diamonds and Cu/Cr-coated diamonds. It was observed that the debonding behavior varied as a result of the differences in the coefficients of thermal expansions (CTEs) among Cu, diamond, and Cr. Moreover, the separation of interfaces had a direct influence upon the equivalent stress state of the Cu-matrix, since diamond particles only deformed elastically. It was revealed through a fully coupled thermo-mechanical FE analysis that repeated heating and cooling cycles resulted in an extremely high stress state within the Cu-matrix along the diamond interface. Since these stresses lead to interfacial debonding, their computation through numerical means may help in determining the service life of heat sinks for a given application beforehand.

Tech Support

Original Source

DOI: https://doi.org/10.3390/ma10070739

References

2011 - Enhanced thermal conductivity in copper matrix composites reinforced with titanium-coated diamond particles [Crossref]
2011 - Effect of coating on the microstructure and thermal conductivities of diamond-Cu composites prepared by powder metallurgy [Crossref]
2010 - Thermal conductivity of SPS consolidated Cu/diamond composites with Cr-coated diamond particles [Crossref]
2009 - Effect of carbide formers on microstructure and thermal conductivity of diamond-Cu composites for heat sink materials [Crossref]
2013 - Thermal conductivity of Cu/diamond composites prepared by a new pretreatment of diamond powder [Crossref]
2012 - Effect of molybdenum as interfacial element on the thermal conductivity of diamond/Cu composites [Crossref]
2014 - Optimization of sintering parameters for diamond-copper composites in conventional sintering and their thermal conductivity [Crossref]
2010 - Thermal properties of diamond-particle-dispersed Cu-matrix-composites fabricated by spark plasma sintering (SPS) [Crossref]
2013 - Preparation of copper-diamond composites with chromium carbide coatings on diamond particles for heat sink applications [Crossref]
2012 - High thermal conductivity composite of diamond particles with tungsten coating in a copper matrix for heat sink application [Crossref]