Abstract: High strength materials are prone to failure in presence of flaws/cracks and this is expressed through the fracture toughness of the material. In fracture base design, the structure should be designed such that for a detectable minimum/or design allowable flaw size the structure under given service condition, the stress intensity factor (K) at the crack tip should always be less than KIc, the plane strain fracture toughness. In view of the sensitiveness of the parameter to the material conditions in terms of heat treatment, grain size, etc. it has become generally necessary to confirm the achieved KIc with respect to what is required by the design. It has been found extremely difficult and impractical to follow standard tests for KIc determination especially at various stages of fabrication/quality control, in view of involved procedures, for testing and to meet the validity conditions of the test. In fracture toughness testing, the Compact Tension (CT) specimen is recommended as one of the standard specimens. Many times the test becomes invalid as per ASTM E 399 standard. Since fracture toughness testing is a costly affair, it is preferable to minimize the number of repeat tests. A simple J-integral method is adopted for assessing the fracture toughness from the invalid test data of standard CT specimens.
Introduction
The safety of the structural component in the absence of cracks can be assured if the stress under service loads is less than the yield strength or 0.2% proof stress (σys)/ultimate tensile strength (σult) of the material, where as in the presence of cracks, the crack-tip stress intensity factor (K) should be less than the fracture toughness (KIc) of the material. Structural components generally contain crack- like defects which are either inherent in the material or introduced during the fabrication process. These cracks usually have sharp edges and are sensitive to initiation of crack growth and fracture. Thus, the fracture toughness of the material used in the structure is a key input for failure assessment.
Material properties such as fracture toughness are variable and a consumer/client may wish to satisfy him-self that the properties of a particular batch of material or component are adequate.
| Fig. 1: | Standard CT specimen and the crack mouth opening displacement location (front face displacement), VFF |
This is normally achieved by testing limited number of samples and assessing the results against a preset criterion to decide whether the material is acceptable. Selection of suitable criterion for choosing fracture toughness value for use in crack assessment or for accepting/rejecting a material is essential to minimize the “consumer’s risk” (risk of accepting bad material) and “producer’s risk” (risk of rejecting good material).
Fracture Toughness (KIc) Evaluation
In fracture toughness testing, the Compact Tension (CT) specimen (Fig.
1) is recommended as one of the standard specimens by the ASTM E24 task
group. The load-displacement curves in general are not perfectly elastic but
exhibit different degrees of non-linearity (Fig. 3). After
considerable experimentation, ASTM E 399 standard (1992) suggested the load
PQ at a 5% secant offset to define KQ as the critical
stress intensity factor at which the crack reaches an effective length, aeff,
equal to 2% greater than the initial crack length a0. To establish
that valid plane strain fracture toughness KIc has been determined,
it is necessary to calculate the ratio Pmax/PQ where Pmax
is the maximum load sustained by the specimen. If
| (1) |
Then the test is invalid because it is possible that KQ is not representative of the plane strain fracture toughness (KIc). If this ratio does not exceed 1.1, we proceed to calculate 2.5(KQ/σys)2, in which, σys is the 0.2% proof-stress or yield strength of the material. If
| (2) |
Then the plane strain fracture toughness,
| (3) |
Otherwise, the test is not a valid KIc test.
| Fig. 2: | Modified CT specimen showing crack opening displacement measurement locations using the load points, VLP and load line displacement, VLL |
To satisfy the requirement of conditions in Eq. (2), it is necessary to use a larger specimen, the size of which can be estimated on the basis of the evaluated KQ.
The available material from the actual hardware of the structural components may not always have sufficient thickness to make standard CT specimens for testing. If KQ is invalid, the strength ratio, R, is a useful comparative measure of the toughness of the material when the specimens tested are of the same size and that size is insufficient to produce a valid KIc. The strength ratio, R, for the CT specimen is (ASTM, 1992).
| (4) |
Here, W is the width of the CT specimen
The above validity conditions when met in the actual specimen ensure that a truly plane strain condition is existing at the crack-tip. If, however, any one of the validity conditions is not met, the test is termed “invalid” and the test is to be discarded. A retest is advised after incorporating suitable changes in the geometry of the specimen. It is quite often possible that due to the above strict validity conditions, the borderline cases are also termed as invalid and reasonably valid data is discarded just because the validity conditions are not meeting by a whisker. Fracture toughness testing is very expensive as it involves fabrication of very complex specimen like Compact Tension (CT) specimen and the equally complicated test procedure that involves fatigue pre-cracking under precisely controlled loading conditions, fracture testing, crack length measurement, etc. All this makes the test very specialized and losing the valuable data, time and material as well as the number for retests should be minimized under all circumstances.
Generation of J-Resistance Curve
For the case of elastic-plastic behavior, the fracture toughness is best
characterized by the J-resistance curve. For fracture toughness evaluation,
the ASTM standard E 1820 (2001) specifies a fairly elaborate procedure to establish
the J-resistance curve and thereupon evaluate the JIc value.
| Fig. 3: | Principal types of load, (P) versus crack opening displacement, (VFF) curves in standard KIc test |
The procedure calls for generating load versus load-line displacement curve when a fatigue pre-cracked specimen is incrementally loaded under displacement control. The crack extension occurring during the incremental loading can be obtained by different techniques like, heat tinting multiple specimens, unloading compliance and potential difference method. The unloading compliance method is most widely used because of its simplicity, accuracy and above all the need for just a single specimen to get the JIc value.
The experimental determination of J-resistance curve requires that the displacement be measured at the load point (VLP, Fig. 2). Because of practical difficulty in measuring VLP, the ASTM standard (2001) proposed that the displacement be measured at the load line (VLL, Fig. 2) with the assumption that the latter is an adequate approximation for VLP. Therefore the CT specimen of E399 standard is modified by enlarging the notch area to accommodate the clip gauge in the load line (Fig. 2). This necessitated the increase in the spacing of loading pin holes. Many investigators later have suggested that this extra machining of the specimen is not required and that the crack mouth opening displacement (CMOD) value (VFF, Fig. 1) is sufficient to develop the J-resistance curve.
Objective of the Present Study
The objective of the present study is to analyze the fracture toughness
data recorded in a standard KIc test. This research presents a simple
J-integral method to assess the fracture toughness from the invalid test data
of CT specimens made of different high strength materials.
Load-line Displacement Evaluation for Compact Tension Specimens
Newman (1979) and Orange (1982) have presented analytical results at different
displacement measurement locations in CT specimens for developing J-resistance
curves. It is noted that the crack front face opening displacement, VFF
provides an approximation to the load point displacement VLP.
After examining the extensive experimental data, Orange has proposed the following empirical expression for VLL in terms of VFF:
| (5) |
| Fig. 4: | Comparison of experimental values of load line displacement (VLL) with those obtained from Eq. 5 and 6 for AA7075-T651 Aluminum alloy |
| Fig. 5: | Comparison of experimental values of load line displacement (VLL) with those obtained from Eq. 5 and 6 for AA2024-T351Aluminum alloy |
| Fig. 6: | Comparison of experimental values of load line displacement (VLL) with those obtained from Eq. (5) and (6) for AISI 304 Steel |
Equation (5) was found to be accurate to within 1% in the range: 0.35≤(a/W)≤0.80. Finite Element Analysis (FEA) results of Neale (1975) indicate a factor of 0.77 to relate VFF to VLL. Hiser and Loss (1985) have examined the variability and applicability of displacements measured at various locations on CT specimens. They found that the average deviation of JIc values evaluated using VFF from the standard JIc values evaluated from VLL was 8% and the maximum deviation was 16%. Finally, they concluded that VFF could be used to generate the J-resistance curve equivalent to that determined using VLL. Landes (1980) suggested a proportionality factor of 0.727 between VLL and VFF that is valid in the range: 0.5≤a/w≤0.75
Rao and Acharya (1986, 1992) have presented a relation between VLL and VFF as:
| (6) |
Here, Z is the distance from the load line to the point of the front-face displacement measurement (Fig. 1).
The recorded load-line displacement values (Newman, 1985) of compact tension specimens having different W/B ratios (16, 8 and 4) made of three materials (namely AA2024-T351, AA7075-T651 and AISI 304 steel) are compared with those obtained from Eq. (5) and (6). For all the three specimen configurations, results obtained from Eq. (5) and (6) correlate well with the experimental results of VLL Fig. (4-6).
| Fig. 7: | Comparison of load -line displacement (VLL) from the recorded front-face displacement (VFF) of standard CT specimens of three materials |
The results of Eq. 6 deviate from the test values by a maximum of 8.6% and on average by 4.4%. The results of Eq. (5) and (6) shown in Fig. 7 for all the three materials, match within -3 to 1.4%.
A Simple Procedure for Generation of J-Resistance Curve from Test Data of
Standard CT Specimens
This section provides a simple procedure for generating J-resistance curve
from the recorded front-face displacement (VFF) of the standard CT
specimen that is generally used for KIc evaluation. While generating
J-resistance curve, Eq. (6) is used to estimate the load line
displacement (VLL) values from the measured front-face displacement
(VFF) values of the standard CT specimen (Fig. 1).
For any point i on the load (P) versus VFF curve, the crack length ai can be obtained from Sexena and Hudak (1978).
| (7) |
Where
| (8) |
Here Pi and VFF are, respectively the load and front face displacement at the point (i) and E is the Young’s modulus.
Crack extension, da, due to increase in load is given by
| (9) |
Here a0 is the initial crack length.
To account for various uncertainties in testing, Modulus E can be replaced by an effective modulus EM given by
| (10) |
Where
Equation (7) gives the crack length (a) corresponding to any point on P versus VFF curve. Using the value of a in Eq. (6) VLL can be calculated. Thus, P versus VLL curve can be generated from the experimental P versus VFF curve of the standard CT specimen.
The area (A) under P versus VFF curve at selected points is used to evaluate the J-integral value (Rice et al., 1973):
| (11) |
Using the values of J and da from Eq. (9) and (11), the J-resistance curve is generated and JIQ is evaluated as per the ASTM standard E1820 (ASTM, 2000). The fracture toughness (KJQ) corresponding to JIQ is obtained from
| (12) |
Here JIQ is the value of J-integral at the intersection of 0.2 mm exclusion line and J-resistance curve and v is the Poisson’s ratio.
Results and Discussion
Following the procedure given in the preceding section, J-resistance curves were generated from the load (P) versus front-face displacement (VFF) curves of the standard CT specimens. Fracture toughness assessments were carried out considering the test data of three materials, namely, M250 maraging steel (parent and weld-metal), high strength low-alloy (HSLA) steel and Ti-6Al-4V alloy.
Fig. 8 shows the load P versus VFF curve from the recorded data of a M250 grade maraging steel CT specimen. The corresponding load P versus VLL curve is also shown in Fig. 8. The load P versus VFF curve is of type I (as per ASTM E 399, Fig. 3), exhibiting smooth curve from linear portion to the maximum load point (without any pop-in). As expected, the load P versus VLL curve is shifted to the left of the load P versus VFF curve. Figure 9 shows the J-resistance curve developed from the load P versus VFF recorded data. Table 1 gives the fracture analysis results for the three materials.
Table 2 shows the comparison between the initial measured crack length, a0 and the crack length, a0-e estimated using Eq. (7). The a0-e is calculated at the point of deviation from linearity on the P-VLL curve and initial measured crack length is from the broken halves of the test specimen measured under a low power microscope at multiple locations as defined in the standard E399.
| Fig. 8: | Typical Load vs COD (P-VFF) curve from plane strain fracture toughness test for M250 maraging steel and the corresponding P-VLL curve developed from it |
| Table 1: | Fracture analysis results of different materials |
| Note: * Thin specimens; + Thick specimens; Width (W) = 2B, for all specimens; andRE % = {(KJQ-KQ)/KQ}*100 | |
| Fig. 9: | J-da curve developed from the recorded P-VFF curve for M250 grade maraging steel. Inset shows the magnified view of the box A |
| Table 2: | Comparison of the initial measured crack length (ap) and the initial crack length (ao-e) estimated using Eq. (7) |
The correlation is excellent, the deviation being within ±5%. The discrepancy in values of KJQ and KQ may be due to the following reasons.
The KIc evaluation is based on the load PQ at 2% crack extension, whereas da values in Table 2 show slightly higher or lower values than 2% crack extension. The value of KJQ is dependent on the relation (1) for thick and thin specimens. Most of the results demand higher thickness specimens for obtaining the valid KIc value. Hence, 7.5 mm thick specimens in the present study are considered as thin specimens. The fracture analysis results of KJQ are found to be within ±5% of the KQ values.
Concluding Remarks
The J-resistance curve can be generated from the load versus crack mouth opening displacement data of standard CT specimens. There is no need to incorporate additional machining in the CT specimens to provide for VLL recording. The J-integral approach will be useful for fracture toughness assessment. The method, however, is applicable to the cases in which the load versus the CMOD curve is of type I and shows gradual curvature from linear to the maximum load point. The KJQ value evaluated from this approach can be used as an indication of fracture toughness of the material provided the value does not differ by more than ±10% from the experimentally evaluated plane strain fracture toughness for that material. Based on such a condition, the procedure described herein can be used for material qualification purposes thus minimizing the number of retests.
Acknowledgements
The authors are grateful to Mr. M.C. Mittal [Group Director, Materials and Metallurgy Group, Vikram Sarabhai Space Centre (VSSC), Trivandrum], for making useful comments/suggestions during the preparation of this article. They wish to thank Dr. K.N. Ninan (Deputy Director, VSSC) for encouragements and Dr. B.N. Suresh (Director, VSSC) for giving permission to publish this article.