Gurson Model (Ductile Fracture)
Gurson Model (Ductile Fracture): Theoretical Foundations
What is the Gurson Model?
Professor, is the Gurson model a model for ductile fracture?
Gurson Model (1977) describes the ductile fracture (void nucleation, growth, coalescence) of metals. The volume fraction $f$ of internal micro-voids affects the material's yield condition.
The void volume fraction $f$ is included in the yield surface!
As $f$ increases, the yield surface contracts โ material softens โ eventually fractures at $f = f_F$. It represents material degradation at the continuum level due to void growth.
GTN Model (Modified Gurson)
Tvergaard and Needleman (1984) modified Gurson's model to create the practical GTN (Gurson-Tvergaard-Needleman) Model. They added correction parameters $q_1, q_2, q_3$.
Summary
The Doctoral Thesis Origin of the Gurson Model
Arthur L. Gurson first published his model for ductile fracture via void growth in his 1975 Brown University doctoral thesis titled "Plastic Flow and Fracture Behavior of Ductile Materials Incorporating Void Nucleation, Growth, and Coalescence." The 1977 paper published in the Journal of Engineering Materials and Technology analytically derived the yield function from the upper bound theorem for porous metals containing spherical voids. This rigorous mechanical derivation is a major feature of the Gurson model.
Computational Methods for Gurson Model (Ductile Fracture)
GTN in FEM
```
*POROUS METAL PLASTICITY
q1, q2, q3
*POROUS FAILURE CRITERIA
f_N, epsilon_N, s_N, f_0, f_c, f_F
```
LS-DYNA: *MAT_120 (GTN).
Summary
GTN Extensions and Tvergaard Constants
The Gurson model evolved into the GTN model (Gurson-Tvergaard-Needleman) when Tvergaard (1981) introduced empirical correction coefficients qโ, qโ, qโ. Typical values are qโ=1.5, qโ=1.0, qโ=qโยฒ=2.25, widely applied to Aluminum and Steel. Furthermore, Needleman & Tvergaard (1984) added the "critical void fraction f*" and a fracture acceleration function, resulting in the current standard GTN model form capable of representing rapid ductile fracture (void coalescence).
Gurson Model (Ductile Fracture) in Practice
GTN in Practice
Used for fracture prediction in sheet metal forming, ductile tearing of nuclear pressure vessels, and ductile fracture of pipelines.
Practical Checklist
Ductile Rupture Analysis of Oil Pipelines
The Gurson model is utilized in burst test analysis for oil and gas pipelines conforming to API 5L standards. DNV-ST-F101 (subsea pipeline standard) recognizes the complementary use of virtual experiments using the GTN model for the two-stage evaluation of plastic collapse and ductile rupture, positioning it as a tool to reduce the number of actual hydrostatic burst tests (costing tens of millions of yen each). Its effectiveness has been confirmed particularly in rupture evaluation of high-strength steel grades X80 and X100.
Gurson Model (Ductile Fracture): Software & Solver Comparison
Tools
Comparison of Abaqus GTN and LS-DYNA MAT224
In Abaqus, the GTN model is defined with the "POROUS METAL PLASTICITY" keyword, directly inputting qโ, qโ, fโ, f_N, etc. In LS-DYNA, equivalent functionality is implemented as MAT_GURSON (Material 120), and since 2020, MAT_MODIFIED_GURSON (Material 220) has been added, providing full GTN extension capabilities. HyperWorks/OptiStruct also began supporting GTN materials in 2022, offering the unique feature of coupling topology optimization with ductile fracture evaluation.
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