Fracture Toughness Fracture toughness is an indication of the amount of stress required to propagate a preexisting flaw. It is a very important material property since the occurrence of flaws is not completely avoidable in the processing, fabrication, or service of a material/component. Flaws may appear as cracks, voids, metallurgical inclusions, weld defects, design discontinuities, or some combination thereof. Since engineers can never be totally sure that a material is flaw free, it is common practice to assume that a flaw of some chosen size will be present in some number of components and use the linear elastic fracture mechanics (LEFM) approach to design critical components. This approach uses the flaw size and features, component geometry, loading conditions and the material property called fracture toughness to evaluate the ability of a component containing a flaw to resist fracture. A parameter called the stress-intensity factor (K) is used to determine the fracture toughness of most materials. A Roman numeral subscript indicates the mode of fracture and the three modes of fracture are illustrated in the image to the right. Mode I fracture is the condition in which the crack plane is normal to the direction of largest tensile loading. This is the most commonly encountered mode and, therefore, for the remainder of the material we will consider KI The stress intensity factor is a function of loading, crack size, and structural geometry. The stress intensity factor may be represented by the following equation:
Where: KI is the fracture toughness in s is the applied stress in MPa or psi is the crack length in meters or inches a B
is a crack length and component geometry factor that is different for each specimen and is dimensionless.
Role of Material Thickness Specimens having standard proportions but different absolute size produce different values for KI. This results because the stress states adjacent to the flaw changes with the specimen thickness (B) until the thickness exceeds some critical dimension. Once the thickness exceeds the critical dimension, the value of KI becomes relatively constant and this value, KIC , is a true material property which is called the planestrain fracture toughness. The relationship between stress intensity, KI, and fracture toughness, KIC, is similar to the relationship between stress and tensile stress. The stress intensity, KI, represents the level of “stress” at the tip of the crack and the fracture toughness, KIC, is the highest value of stress intensity that a material under very specific (plane-strain) conditions can withstand without fracture. As the stress intensity factor reaches the KIC value, unstable fracture occurs. As with a material’s other mechanical properties, KIC is commonly reported in reference books and other sources.
Plane-Strain and Plane-Stress When a material with a crack is loaded in tension, the materials develop plastic strains as the yield stress is exceeded in the region near the crack tip. Material within the crack tip stress field, situated close to a free surface, can deform laterally (in the z-direction of the image) because there can be no stresses normal to the free surface. The state of stress tends to biaxial and the material fractures in a characteristic ductile manner, with a 45o shear lip being formed at each free surface. This condition is called “plane-stress" and it occurs in relatively thin bodies where the stress through the thickness cannot vary appreciably due to the thin section.
Plane Strain - a condition of a body in which the displacements of all points in the body are parallel to a given plane, and the values of theses displacements do not depend on the distance perpendicular to the plane Plane Stress – a condition of a body in which the state of stress is such that two of the principal stresses are always parallel to a given plane and are constant in the normal direction.
However, material away from the free surfaces of a relatively thick component is not free to deform laterally as it is constrained by the surrounding material. The stress state under these conditions tends to triaxial and there is zero strain perpendicular to both the stress axis and the direction of crack propagation when a material is loaded in tension. This condition is called “plane-strain” and is found in thick plates. Under plane-strain conditions, materials behave essentially elastic until the fracture stress is reached and then rapid fracture occurs. Since little or no plastic deformation is noted, this mode fracture is termed brittle fracture.
Plane-Strain Fracture Toughness Testing When performing a fracture toughness test, the most common test specimen configurations are the single edge notch bend (SENB or three-point bend), and the compact tension (CT) specimens. From the above discussion, it is clear that an accurate determination of the planestrain fracture toughness requires a specimen whose thickness exceeds some critical thickness (B). Testing has shown that plane-strain conditions generally prevail when:
Where: B is the minimum thickness that produces a condition where plastic strain energy at the crack tip in minimal KIC is the fracture toughness of the material sy is the yield stress of material
When a material of unknown fracture toughness is tested, a specimen of full material section thickness is tested or the specimen is sized based on a prediction of the fracture toughness. If the fracture toughness value resulting from the test does not satisfy the requirement of the above equation, the test must be repeated using a thicker specimen. In addition to this thickness calculation, test specifications have several other requirements that must be met (such as the size of the shear lips) before a test can be said to have resulted in a KIC value. When a test fails to meet the thickness and other test requirement that are in place to insure plane-strain condition, the fracture toughness values produced is given the designation KC. Sometimes it is not possible to produce a specimen that meets the thickness requirement. For example when a relatively thin plate product with high toughness is being tested, it might not be possible to produce a thicker specimen with plain-strain conditions at the crack tip. To proposed ASTM test method specifies minimum specimen thicknesses and crack lengths required to obtain acceptable Kic values from tests of SENB and CT specimens.
Plane-Stress and Transitional-Stress States For cases where the plastic energy at the crack tip is not negligible, other fracture mechanics parameters, such as the J integral or R-curve, can be used to characterize a material. The toughness data produced by these other tests will be dependent on the thickness of the product tested and will not be a true material property. However, plane-strain conditions do not exist in all structural configurations and using KIC values in the design of relatively thin areas may result in excess conservatism and a weight or cost penalty. In cases where the actual stress state is plane-stress or, more generally, some intermediate- or transitionalstress state, it is more appropriate to use J integral or R-curve data, which account for slow, stable fracture (ductile tearing) rather than rapid (brittle) fracture. For isotropic, perfectly brittle, linear elastic materials, the J-integral can be directly related to the fracture toughness.
For plane strain, under Mode I loading conditions, this relation is
Uses of Plane-Strain Fracture Toughness KIC values are used to determine the critical crack length when a given stress is applied to a component.
Where: sc
is the critical applied stress that will cause failure
KIC
is the plane-strain fracture toughness
Y
is a constant related to the sample's geometry is the crack length for edge cracks or one half crack length for internal crack
a
KIC values are used also used to calculate the critical stress value when a crack of a given length is found in a component.
Where: a
is the crack length for edge cracks or one half crack length for internal crack
s
is the stress applied to the material
KIC
is the plane-strain fracture toughness
Y
is a constant related to the sample's geometry
Orientation The fracture toughness of a material commonly varies with grain direction. Therefore, it is customary to specify specimen and crack orientations by an ordered pair of grain direction symbols. The first letter designates the grain direction normal to the crack plane. The second letter designates the grain direction parallel to the fracture plane. For flat sections of various products, e.g., plate, extrusions, forgings, etc., in which the three grain directions are designated (L) longitudinal, (T) transverse, and (S) short transverse, the six principal fracture path directions are: L-T, L-S, T-L, T-S, S-L and S-T.
Stress-intensity Factor (K) is a quantitative parameter of fracture toughness determining a maximum value of stress which may be applied to a specimen containing a crack (notch) of a certain length. Depending on the direction of the specimen loading and the specimen thickness, four types of stress-intensity factors are used: KC, KIC KIIC KIIIC. KC – stress-intensity factor of a specimen, thickness of which is less than a critical value. KC depends on the specimen thickness. This condition is called plane stress.
KIC,KIIC, KIIIC – stress-intensity factors, relating to the specimens, thickness of which is above the critical value therefore the values of KIC KIIC KIIIC do not depend on the specimen thickness. This condition is called plane strain. KIIC and KIIIC – stress-intensity factors relating to the fracture modes in which the loading direction is parallel to the crack plane. These factors are rarely used for metals and are not used for ceramics; KIC – plane strain stress-intensity factor relating to the fracture modes in which the loading direction is normal to the crack plane. This factor is widely used for both metallic and ceramic materials. KIC is used for estimation critical stress applied to a specimen with a given crack length: σC ≤KIC /(Y(π a)½) Where KIC – stress-intensity factor, measured in MPa*m½; σC– the critical stress applied to the specimen; a – the crack length for edge crack or half crack length for internal crack; Y – geometry factor.
Impact test Impact test is used for measuring toughness of materials and their capacity of resisting shock. In this test the pendulum is swing up to its starting position (height H ) and then it is allowed to strike the notched specimen, fixed in a vice. The pendulum fractures the specimen, spending a part of its energy. After the fracture the pendulum swings up to a height H. The impact toughness of the specimen is calculated by the formula: a = A/ S Where a-impact toughness,
A – the work, required for breaking the specimen ( A = M*g*H0–M*g*H), M - the pendulum mass, S - cross-section area of the specimen at the notch. One of the most popular impact tests is the Charpy Test, schematically presented in the figure below:
The hammer striking energy in the Charpy test is 220 ft*lbf (300 J).
Test techniques: 1-Compact tension (CT)
2- CHARPY impact specimen (
Single edge notched bend (SENB), single edge notched tension (SENT).)
1-http://www.ndted.org/EducationResources/CommunityCollege/Materials/Mechanical/FractureTou ghness.htm 2-http://www.twi.co.uk/content/kscsw011.html 3-http://www.twi.co.uk/content/kscsw011.html
Background The resistance to fracture of a material is known as its fracture toughness. Fracture toughness generally depends on temperature, environment, loading rate, the composition of the material and its microstructure, together with geometric effects (constraint).[1] These factors are of particular importance for welded joints, where the metallurgical and geometric effects are complex[2,3] Fracture toughness is a critical input parameter for fracture-mechanics based fitness-for-service assessments. Although fracture toughness can sometimes be obtained from the literature, or materials properties databases, it is preferable to determine this by experiment for the particular material and joint being assessed. Various measures of 'toughness' exist, including the widely used but qualitative Charpy impact test. Although it is possible to correlate Charpy energy with fracture toughness, a large degree of uncertainty is associated with correlations because they are empirical. It is preferable to determine fracture toughness in a rigorous fashion, in terms of K (stress intensity factor), CTOD (crack tip opening displacement), or J (the J integral); see also What is a fracture toughness test? Standards exist for performing fracture mechanics tests, with the most common specimen configuration shown in Fig.1 (the single-edge notch bend SENB specimen, sometimes referred as a SE(B) specimen). A sharp fatigue crack is inserted in the specimen, which is loaded to failure. The crack driving force is calculated for the failure condition, giving the fracture toughness.
Fig.1. Fracture mechanics testing
Standards Various national Standards have been developed for fracture toughness testing: •
The British Standard BS 7448[4] includes four parts, for testing of metallic materials, including parent materials (Part 1), weldments (Part 2), high strain rates (dynamic fracture toughness testing, Part 3), and resistance curves (R-curves for ductile tearing, Part 4). BS 7448: Part 2 is the first Standard worldwide to apply specifically to weldments.
•
A series of American standards (ASTM) cover K, CTOD, J testing, ASTM E1290 (CTOD testing), ASTM E1820 (K, J & CTOD, including R-curves) and ASTM E1921 (J testing to determine T0 for ferritic steels). None specifically address testing of welds. ASTM E1823 provides a useful summary of terminology.[5-9]
•
A series of international (ISO) standards are being developed. ISO 12135 covers all aspects of fracture testing (K, J-integral & CTOD) of plain material. Standards are being prepared on testing of welds (ISO/FDIS 15653) and stable crack growth in low constraint specimens (ISO/22889). The latter is mainly concerned with testing thin, sheet material.
•
The European Structural Integrity Society (ESIS) has published procedures for R-curve and standard fracture toughness testing of metallic materials.[10-11] A draft unified testing procedure (ESIS P3-04), which includes weld testing, is being developed. (These are not standards in the usual sense, but rather testing protocols that have been agreed by experts. Unfortunately, currently there is no formal mechanism for keeping these protocols up to date). Increasing use is being made of single edge notch tension (SENT or SE(T)) specimens to determine fracture toughness of girth welds in submarine pipelines. Currently, there is no testing standard but a DNV recommended practice does provide a testing protocol [12]. This is designed for ductile materials and the protocol describes a method for the determination of a J R-curve.
•
Although different standards have historically been published for determining K, CTOD and Jintegral, the tests are very similar, and generally all three values can be established from one test. See Are there any differences between fracture toughness tests carried out to BS7448 and E1820?
Test specimens The most widely used fracture toughness test configurations are the single edge notch bend (SENB or three-point bend), and the compact (CT) specimens, as shown in Fig.2. The compact specimen has the advantage that it requires less material, but is more expensive to machine and more complex to test compared with the SENB specimen. Also, special requirements are needed for temperature control (e.g. use of an environmental chamber). SENB specimens are typically immersed in a bath for low temperature tests. Although the compact specimen is loaded in tension, the crack tip conditions are predominantly bending (high constraint). If limited material is available, it is possible to fabricate SENB specimens by welding extension pieces (for the loading arms) to the material sample. (Electron beam welding is typically used, because the weld is narrow and causes little distortion).
Fig.2. Examples of common fracture toughness test specimen types
Other specimen configurations include centre-cracked tension (CCT) panels, single edge notch tension (SENT) specimens, and shallow-crack tests. These specialised tests are associated with lower levels of constraint, and can be more structurally representative than standard SENB or CT specimens. SENT specimens are being used to determine fracture toughness of pipeline girth in submarine pipelines, especially where the installation method involves plastic straining. Further information can be found in a DNV recommended practice [12] and Appendix A of a DNV standard [13]. The primary purpose of the tests is to define flaw acceptance criteria when the results are used with an appropriate assessment procedure. The position and orientation of the specimen is important. In particular, the location and orientation of the notch is critical, especially for welded joints. Typically, the notch (fatigue precrack) is positioned such that a chosen microstructure is sampled. The orientation of the notch is defined with respect to either the weld axis for welded joints, or the rolling direction or forging axis for other components. In standard SENB & C T specimens (see Fig.1), the notch depth is within the range 45-70% of the specimen width, W, giving a lower-bound estimate of fracture toughness, because of the high level of crack tip constraint generated by the specimen design. A notch is machined into the fracture toughness specimen blank, following which a fatigue crack is grown by applying cyclic loading to the specimen. In order to minimise the time spent in fatigue pre-cracking, specialised high frequency resonance or servo-hydraulic machines are often used for this process. Since specimens taken from as-welded joints will contain residual stresses arising from the welding process, there is a risk of non-uniform fatigue pre-cracks which would invalidate the test result. To counter this, various options are recommended in BS7448 Part2. The most commonly used method which has also been found to provide the most consistent results is local compression. This involves controlled plastic compression of the sides of the specimen after notching but before fatigue pre-cracking. The fracture mechanics test standards include many checks to ensure that results are credible. These include restrictions on the fatigue crack size, plane and shape, together with limitations on
the maximum allowable fatigue force (this is to ensure that the crack-tip plastic zone produced during fatigue pre-cracking is small in comparison with the plastic zone produced during testing). Many of these checks can only be performed after testing.
Instrumentation and loading During fracture toughness testing, the force applied to the specimen and specimen displacements and loading rate (using load cells and displacement transducers), together with the temperature are recorded. One of the displacements is the crack-mouth opening. This is measured using a clip gauge either attached to knife edges mounted at the crack mouth (see Fig.1) or integral knife edges machined into the notch. These gauges comprise two cantilevered beams on which are positioned four strain gauges. By measuring the elastic strains and calibration crack-mouth opening displacement is obtained. Analysis of the relationship between applied force and crack mouth opening displacement form the test enables fracture toughness to be determined in terms of K, CTOD and J-integral. Fracture toughness tests are performed in universal hydraulic test machines, generally using displacement control.
Fracture toughness parameters The following are the fracture toughness parameters commonly obtained from testing •
K (stress intensity factor) can be considered as a stress-based estimate of fracture toughness. It is derived from a function which depends on the applied force at fracture. K depends on geometry (the flaw depth, together with a geometric function, which is given in test standards for each test specimen geometry).
•
CTOD or (crack-tip opening displacement) can be considered as a strain-based estimate of fracture toughness. However, it can be separated into elastic and plastic components. The elastic part of CTOD is derived from the stress intensity factor, K. In some standards, the plastic component of CTOD is obtained by assuming that the specimen rotates about a plastic hinge. The plastic component is derived from the crack mouth opening displacement (measured using a clip gauge). The position of the plastic hinge (defined by rp ) is given in test standards for each specimen type. Alternative methods exist for estimating CTOD, which make no assumption regarding the position of the plastic hinge. These require the determination of J from which CTOD is derived.[6,7] CTOD values determined from formulations assuming a plastic hinge[4] may differ from those determined from J.[6,7]
•
J (the J-integral) is an energy-based estimate of fracture toughness. It can be separated into elastic and plastic components. As with CTOD, the elastic component is based on K, while the plastic component is derived from the plastic area under the force-displacement curve.
It should be noted that all three fracture parameters can be related to one another. However, the relationship is not unique and depends on material tensile properties and specimen geometry.
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References Items 1-3 are not in the public domain but are available to TWI Industrial Member companies. 1. M G Dawes: 'An Introduction to K, CTOD and J Fracture Mechanics Analyses and Toughness, and the Application of these to Metal Structures'. 2. H G Pisarski: 'Update on Fracture Toughness Test Methods for Welded Joints'. 3. H G Pisarski: 'A Review of HAZ Toughness Evaluation'. 4. BS7448: 'Fracture Mechanics Toughness Tests' • Part 1:1991: 'Method for determination of Kic, Critical CTOD and Critical J values of metallic material'. • Part 2: 1997: 'Method for Determination of Kic, Critical CTOD and Critical J Values of Welds in Metallic Materials'. • Part 3: 2005 'Method for determining dynamic fracture toughness' (to be published in 2005) • Part 4 1997: 'Method for Determination of Fracture Resistance Curve and Initiation values for Stable Crack Extension in Metallic Materials'. British Standards Institute, London.
5. ASTM E399-09: 'Standard Test Method for Plane Strain Fracture Toughness of Metallic Materials'. American Society of Testing and Materials, Philadelphia, 2009. 6. ASTM E1290-09: 'Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement'. American Society of Testing and Materials, Philadelphia, 2009 7. ASTM E1820-09: 'Standard Test Method for Measurement for Fracture Toughness'. American Society of Testing and Materials, Philadelphia, 2009. 8. ASTM E1823-09: 'Technology Relating to Fatigue and Fracture Testing'. American Society for Testing and Materials, Philadelphia, 2009. 9. ASTM E1921-09 'Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range'. American Society of Testing and Materials, Philadelphia, 2009 10. ESIS P1-92: 'ESIS Recommendation for Determining the Fracture Resistance of Ductile Materials' European Structural Integrity Society, 1992. 11. ESIS P2-92: 'ESIS Procedure for Determining the Fracture Behaviour of Materials'. European Structural Integrity Society, 1992.
12. DNV-RP-F108: 'Fracture control for pipeline installation methods introducing cyclic plastic strain'. Det Norske Veritas, January 2006. 13. DNV-OS-F101: 'Submarine pipeline systems'. Det Norske Veritas, October 2007.
Collected by: Babak RH
