Measuring and testing – Specimen stress or strain – or testing by stress or strain... – By loading of specimen
Reexamination Certificate
2001-06-25
2003-07-08
Williams, Hezron (Department: 2855)
Measuring and testing
Specimen stress or strain, or testing by stress or strain...
By loading of specimen
C073S799000
Reexamination Certificate
active
06588283
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to methods and apparatus for determining the intrinsic values of fracture toughness K
IC
and mixed mode fracture toughness for various structural materials such as steels, aluminum alloy, ceramics and metal-matrix composites using small spiral-grooved cylindrical specimens and pure torsional loading.
2. Background Information
The present invention determines fracture toughness K
IC
and mixed mode fracture toughness of solid materials utilizing a unique specimen design and loading condition in conjunction with a special finite element program. K
IC
is a material property that describes the material's fracture resistance to brittle fracture initiation under full lateral constraint during static or “quasistatic” loading. The test methods that are currently used in many industries, including the nuclear industry, to evaluate fracture toughness may not fully conform to fracture mechanics theory. This is because the specimen size required to achieve complete control of the plane strain is prohibitively large. Hence, when critical flaw size and/or safe design stress is desired, K
IC
may be inferred from values derived from non-fracture-mechanics methods. Because the indirect methods inevitably contain large uncertainties, a large safety factor must be built into the design. With the invention, K
IC
is determined directly, without interpretation, allowing the uncertainty and safety factor associated with the safety assessment of fracture properties to be minimized.
In the present invention, a right cylindrical specimen having a spiral groove with a 45° pitch is tested under pure torsion. A computer code, TOR3D-KIC, is then used to determine the mode I fracture toughness. Mixed mode fracture toughness values can be derived by varying the spiral pitch. TOR3D-KIC uses three-dimensional finite element techniques to analyze the crack tip opening displacement (CTOD) occurring on a non-coplanar 3-D spiral crack front. Special 3-D finite element meshes, with wedge singular elements at the crack front, were designed to simulate the 3-D spiral crack front and crack propagation orientation during transition phases of fatigue crack growth and the final fracture. Boundary conditions were assigned for the torsional loading configuration. Based on the input of the fracture load and final crack length, the CTOD at the crack flange along the crack front is analyzed and then integrated into the mode I fracture toughness formulation in conjunction with the minimum strain energy criteria.
The method can be used to determine the fracture toughness of graduated materials such as weldments and their heat-affected zones. Thus, the new method should be invaluable for the development of new structural materials and new welding technology, and it can be used in establishing new industry standards and regulatory guidelines.
The testing method that uses conventional compact tension specimens or their variations has a strong theoretical basis for use in determining fracture toughness, K
IC
. However, the downside of the method is the specimen size effect. Valid test result according to ASTM Test Method for Plane-Strain Fracture Toughness of Metallic Materials (E399), requires that both specimen thickness, B, and crack length, a, exceed 2.5(K
IC
/&sgr;
YS
)
2
, where &sgr;
YS
is the 0.2% offset yield strength of the material for temperature and loading rate of the test. If it is not possible to make a specimen from the available material that meets the criterion, then it is not possible to make a valid K
IC
measurement according to this method.
One prior method [Ref. 1] for K
IC
measurement under torsion uses a round specimen with a half penny-shaped crack making a 45° angle with the specimen axis. This is basically a variation of tensile testing with a half penny shaped crack perpendicular to the tensile force. The latter type has been widely used in crack growth studies.
Our recent study [Ref. 2] demonstrated that the specimen size effects could be virtually eliminated using a cylindrical specimen subjected to pure torsion for K
IC
measurements.
REFERENCES
[1] Sweeney, J., “Analysis of a Proposed Method for Toughness Measurements Using Torsion Testing,”
Journal of Strain Analysis,
1985, Vol. 20, No. 1, pp. 1-5.
[2.] Wang, J. A., Liu, K. C., McCabe, D. E., and David, S. A., “Using Torsional Bar Testing to Determine Fracture Toughness,”
Journal of Fatigue
&
Fracture for Engineering Materials and Structures,
2000, Vol. 23, pp. 917-927.
BRIEF SUMMARY OF THE INVENTION
In a first embodiment of the invention, a method of determining fracture toughness K
IC
of a material comprises the steps of providing a cylindrical specimen having a helical groove at a 45° pitch, applying pure torsion to the specimen, measuring the fracture torque, measuring the crack length, and calculating K
IC
from the fracture torque and the crack length.
The calculation of K
IC
is carried out with a computer program which comprises the steps of: establishing a finite element mesh for a cylindrical specimen under pure torsion to generate an equibiaxial tension/compression stress field on ±45°-pitched orthogonal planes of the finite elements along the right conoids, and a plane strain condition is maintained on every plane normal to the helical groove; establishing 3-D isoparametric finite element meshes with singular elements around the 3-D spiral crack front to simulate r
−½
singularity at the crack tip; simulating spiral crack front and crack propagation orientation along the right conoids; prescribing boundary conditions with free axial displacement to simulate pure torsion loading; applying initial end rotation to the finite element model with a given final crack length to determine the corresponding end torque; iterating the end torque step to match the end torque with the measured fracture torque to determine the final end rotation of the finite element model; determining the crack tip opening displacement based on the stress/strain field derived from the calculated final end rotation; verifying that the triaxial stresses and T-stress fields around the crack tip at fracture are positive to ensure a high constraint state is achieved; determining stress intensity factors K
I
, K
II
, and K
III
from the crack tip opening displacement; and utilizing the stress intensity factors K
I
, K
II
, and K
III
information and strain energy density criteria to determine the fracture toughness K
IC
.
In a second embodiment of the invention, a method of determining mixed mode fracture toughness of a material comprises the steps of providing a cylindrical specimen having a helical groove, applying pure torsion to the specimen, measuring the fracture torque, measuring the crack length, and calculating the mixed mode fracture toughness from the fracture torque and the crack length.
The calculation of mixed mode fracture toughness is carried out with a computer program which comprises the steps of: establishing a finite element mesh for a cylindrical specimen under pure torsion to generate an equibiaxial tension/compression stress field on ±45°-pitched orthogonal planes of the finite elements along the right conoids, and a plane strain condition is maintained on every plane normal to the helical groove; establishing 3-D isoparametric finite element meshes with singular elements around the 3-D spiral crack front to simulate r
−½
singularity at the crack tip; simulating spiral crack front and crack propagation orientation along the right conoids; prescribing boundary conditions with free axial displacement to simulate pure torsion loading; applying initial end rotation to the finite element model with a given final crack length to determine the corresponding end torque; iterating the end torque step to match the end torque with the measured fracture torque to determine the final end rotation of the finite element model; determining the crack tip opening displacement based on the stre
Liu Kenneth C.
Wang Jy-An
Martir Lilybett
Spicer James M.
UT-Battelle LLC
Williams Hezron
LandOfFree
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