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This Week's Feature Metal Example

Prediction & Verification of Metal Fracture Toughness Tests Using Non-linear Static Stress-Strain Curve

Figure 1 -  Full Stress-Strain Curve and Crack Tip Deformation [2] (a) Areas Associated With The Uniform (b) A Center Crack in Wide Panel and Non-Uniform Straining 

Safe life prediction of components must be conducted to ensure the life adequacy of parts during service usage. In many cases fracture properties of material are not available because of 1) cost associated with generating fatigue and fracture data, 2) Inability to conduct tests because of time limitation and deadline set forth by the customers, and 3) lack of analytical tools to conduct a comprehensive crack tip stress analysis. 

New material-physics based computational methodologies for assessing the plane-stress and the plane-strain fracture toughness (KC, KIC) and (da/dN versus Delta K curve) of the material have been used successfully in predicting these fracture allowables, knowing only the complete stress-strain behavior of the material of interest. 

Figure 2 - Typical Crack Growth Rate Versus Stress Intensity Range

Farahmand extended the Griffith theory to estimate fracture toughness value of metals from simple uniaxial tensile tests. Figure 1 illustrates the extended Griffith theory and regions of crack tip plastic deformation. Accounting for the energy absorption rate for plastic deformation at the crack tip is calculated and used to establish a relationship between fracture stress and half critical crack length [1]. 

On the other hand, fatigue crack growth properties of the material are determined using the well known Newman Forman and Koening (FNK) equation requiring input from fracture toughness theoretical model. The analytical procedure relies on both implicit and explicit computational schemes and evaluates points in the threshold, Paris, and accelerated regions (Figure 2). 

Once the fracture allowables are determined, the values can be further used to predict the S-N curve of the component using finite element method approach with Virtual Crack Closure Technique (VCCT). The formulation extends to fatigue crack growth and strength life prediction of notched and unnotched components. Scientists at Alpha STAR and TU Delft are extending the algorithm to composites.
Figure 3 - Process and Comparison of Fracture Toughness Versus Thickness [FTD] and da/dN Versus Delta K Curve [FCG] With The Test Data Provided in NASGRO for Ti-6Al-4V (Mill Annealed) [2].

Figure 3 shows the process and comparison of the results obtained using the two methodologies (Fracture Toughness Determination [FTD] and Fatigue Crack Growth [FCG]) for a Titanium alloy. Similar verification has been done with several other pure and alloyed materials, such as Aluminum alloy, Inconel, Steel, and many more. 

Figure 4 - Metallic Center Cracked Panel Subjected to Quasi-Static Fatigue Loading [2]
The virtual testing technique was later used to generate the high cycle fatigue data (the S-N curve). The fracture allowables predicted from the FTD/FCG modules in GENOA for a center-cracked specimen were used to assess the total life of uncracked specimen made of Ti6-4MA and 7075-T6 Titanium and Aluminum alloys, respectively (Figure 4). The panels were subjected to quasi-static fatigue loading using progressive failure analysis in conjunction with Virtual Crack Closure Technique (VCCT) (A link to the past news letter). The comparison of the predicted and test results is tabulated in Table 1 for four tests. 

The capability of the three step approach: 1) Fracture Toughness Determination, 2) Fatigue Crack Growth Determination, and S-N curve Determination was demonstrated Life Assessment of Boeing 747 crown Panel Fuselage Section (Figure 5).

Table 1 - Comparison between Test and Simulation Results for Life Assessment of Metallic Center Cracked Panel, As Shown In Figure 3 [2]
The results validated that the novel Fracture Toughness Determination, Fatigue Crack Growth Determination and Life Assessment Methodologies in GENOA indicating further that GENOA can be reliably used to assess fracture allowables for a materials extremely quickly and with reasonable accuracies. 
Figure 5. Three Step Approach to Assess Life of the Stiffened Curved Panel Made of Aluminum Alloy [2]
In addition, a probabilistic analysis of the fracture toughness and fatigue crack growth can also be performed using the Probabilistic Fracture Toughness (PFTD) and Probabilistic Fatigue Crack Growth (PFCG) modules in GENOA (Figures 6 & 7). The probabilistic capability allows monitoring the sensitivity of the response (KC, KIC, and da/dN versus DK curve) to different input variables [3]. 
Figure 6 - Variation of Fracture Toughness with Variable Thickness [3]
Figure 7 - Variation of Plane Stress (KC) and Threshold (Kth) Fracture Toughness Due to Variations in Material Properties. [3]

Click here to receive demo and presentation of FTD & FCG.



1. Farahmand, B., Fatigue and Fracture Mechanics of High Risk Parts, Chapman and Hall, 1997. 
2. Farahmand, B., Saff, C., Xie, D., and Abdi, F., 2007. Estimation of Fatigue and Fracture Allowables for Metallic Materials Under Cyclic Loading. AIAA-2007-2381. Click here to read technical publication.
3. Farahmand, B., and Abdi, F., 2002. Probabilistic Fracture Toughness, Fatigue Crack Growth Estimation Resulting From Material Uncertainties. ASTM International Paper. Click here to read technical publication.

Click here to read the full technical product data sheet of GENOA.

Did You Know?

Benefits from Virtual Simulation of ASTM Tests

imageVirtual simulation of ASTM tests using GENOA enables the qualification and characterization of aerospace materials. The successful replication of these tests provides the designer and analyst with a reliable tool to evaluate the component performance. Iterative designs can be made with GENOA until satisfactory performance is achieved. This capability eliminates redundant tests thereby expediting the component certification and delivery to market.  For more information on this feature and trying out GENOA through our demos, please contact our sales at

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