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AFGROW | DTD Handbook

Handbook for Damage Tolerant Design

  • DTDHandbook
    • About
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    • Sections
      • 1. Introduction
      • 2. Fundamentals of Damage Tolerance
      • 3. Damage Size Characterizations
      • 4. Residual Strength
      • 5. Analysis Of Damage Growth
      • 6. Examples of Damage Tolerant Analyses
      • 7. Damage Tolerance Testing
        • 0. Damage Tolerance Testing
        • 1. Introduction
        • 2. Material Tests
          • 0. Material Tests
          • 1. Fracture Toughness Testing Methods
            • 0. Fracture Toughness Testing Methods
            • 1. Plane-Strain Fracture Toughness
            • 2. R-Curve
            • 3. Crack Initiation J-Integral
          • 2. Sub-Critical Crack Growth Testing Methods
        • 3. Quality Control Testing
        • 4. Analysis Verification Testing
        • 5. Structural Hardware Tests
        • 6. References
      • 8. Force Management and Sustainment Engineering
      • 9. Structural Repairs
      • 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
      • 11. Summary of Stress Intensity Factor Information
    • Examples

Section Plane-Strain Fracture Toughness

The plane-strain fracture toughness (KIc) measures crack resistance to abrupt fracture under tri-tensile crack tip stress conditions where the constraint against crack tip deformation is maximized.  As such, KIc data represent a lower bound on the fracture toughness that a material might experience under a wide range of cracking and geometric configurations.  The ASTM E399 standard that covers plane-strain fracture toughness of metallic materials  was developed to obtain values of fracture toughness using relatively thick specimens (thus maximizing the crack tip constraint) subjected to quasi-static loading conditions.  The determination of KIc is also covered in the common fracture toughness method ASTM E1820.

A variety of specimen configurations are currently recommended for collecting KIc data, some of which are described in Figure 7.2.1.  The compact tension [C(T)] and the single edge notched bend specimen [SE(B)] were initially the only specimens recommended for the measurements and most laboratories are well equipped to support these tests.  The arc-shaped tension [A(T)], disk-shaped compact tension [DC(T)], and arc-shaped bend [A(B)] specimens have since been added as these configurations evolved to characterize the resistance of specific structural product forms, i.e. tube/pipe type structures and cylindrically shaped bar stock.

It should be noted that ASTM E399 uses linear elastic fracture mechanics as its basis for calculating fracture toughness.  For this reason, specimen sizing requirements are predicated on maintaining a crack tip plastic zone size that is a small fraction of the planar dimensions of the specimen.  The test method is also specific about ensuring that the thickness of a KIc specimen is substantially larger than the crack tip plastic zone size so that a crack tip tri-tensile stress state is established which maximizes the constraint on plastic deformation.  Basically, the specimens are sized so that the dimensions of crack size (a), thickness (B), and remaining ligament size (W-a) are greater than the ratio of 2.5 (KIc/sys)2, i.e., so that


where sys is the 0.2 percent offset yield strength and the KIc value meets all the test criteria.

The procedures for determining fracture toughness outlined in ASTM E1820 are essentially identical to E399 for samples sufficiently thick to provide valid KIc measurements.   The plane-strain crack toughness test is unusual in that there can be no advanced assurance that the fracture toughness established by a given test will be a valid KIc value.  The fracture toughness calculated after a given test must be validated through a series of criteria checks that are thoroughly described in E399 and E1820.  The principle advantage of E1820 is that one can analyze the test information using different criteria to come up with valid toughness measurements if the thickness is too thin for valid KIc values. 

Schematic load-displacement curves representative of the type of behavior exhibited during a test to determine the plane-strain fracture toughness are shown in Figure 7.2.3.  The collection of such load-displacement data is a requirement of most ASTM fracture related standards.  The objective of this test record is to establish the load, PQ, which will be used in the calculations of the test fracture toughness value (KQ), and the level of maximum test load (Pmax).  The test fracture toughness (KQ) is a conditional result that must be validated through checking the size requirements before accepting KQ as a valid plane-strain fracture toughness (KIc) value.  If KQ is a non-valid test result according to ASTM E399, KQ should not be utilized as an estimate for KIc for design purposes since the value may be very non-conservative. 

Figure 7.2.3.  Principal Types of Load-Displacement Records [ASTM 2001]