CN118737345B - A prediction model for crack arrest toughness based on ductile-brittle transition temperature of crack arrest steel - Google Patents
A prediction model for crack arrest toughness based on ductile-brittle transition temperature of crack arrest steel Download PDFInfo
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Abstract
The invention relates to the technical field of material fracture failure research, in particular to a prediction model for fracture toughness based on fracture-stopping steel ductile-brittle transition temperature, which comprises the following specific steps of S1, taking an impact sample in the thickness direction of a high-strength fracture-stopping steel plate, S2, carrying out a series of temperature oscillometric impact tests on the sample, S3, obtaining a fracture initiation ductile-brittle transition temperature K a, S4, obtaining the fracture-stopping toughness K ca of the high-strength fracture-stopping steel through actual measurement, S5, fitting by using the fracture initiation ductile-brittle transition temperature K a and the fracture-stopping toughness K ca to obtain a formula 1:K ca=A+B*Ka, and S6, obtaining the corresponding high-strength fracture-stopping toughness K ca by introducing the fracture initiation ductile-brittle transition temperature K a into a formula 1. The method can simply and effectively predict the crack-arresting toughness of the high-strength crack-arresting steel through the prediction model, does not need to carry out a large number of double tensile tests, saves test time and cost, and has the characteristics of simplicity and high efficiency.
Description
Technical Field
The invention relates to the technical field of material fracture failure research, in particular to a prediction model for fracture toughness based on ductile-brittle transition temperature of fracture-stopping steel.
Background
In the current society, the importance of the ship's crack-stopping ability is not ignored. With the continuous development of global trade and shipping industry, ships are used as main tools for marine transportation, and the safety and reliability of the ships are directly related to the safety of personnel and goods and the protection of marine environment. Therefore, improving the crack-stopping ability of a ship is important for ensuring shipping safety. The ship may face various complex marine environments and climatic conditions during sailing, such as ocean waves, storms, seawater corrosion, etc. These factors may cause cracking or damage to the ship structure, which may cause fracture accidents, and large ships such as container ships, mail wheels, etc., which are required to bear significant weight and pressure during transportation. Therefore, the ship crack-stopping capability has important significance in the current society, and the ship crack-stopping capability is continuously improved by adopting advanced materials and technical means, so that the safe and reliable navigation of the ship in a complex marine environment can be ensured, and a powerful guarantee is provided for the sustainable development of global trade and shipping industry.
The crack-stopping performance of the existing hull steel material is mainly reflected by the crack-stopping toughness and the crack-stopping temperature, and the test of the crack-stopping toughness and the crack-stopping temperature is derived from ESSO test, double tensile test, wide plate tensile test, biaxial tensile test and the like, and the sample preparation of the test method is complex, the test equipment requirement is high, the stress state is complex and the cost of the large-size sample is high. Therefore, a great deal of research is carried out at home and abroad, various correlation models are established about the fracture toughness, the fracture toughness and the small-size sample characterization parameters, such as the correlation model of the fracture toughness and the plastic-free transition temperature, the correlation model of the fracture toughness CAT and the tensile strength R m, the plastic-free transition temperature NDT, the ductile-brittle transition characteristic parameter k and the plate thickness t, the correlation model of the fracture toughness CAT and the carbon equivalent C eq, the tensile strength R m, the ductile-brittle transition characteristic parameter lnk and the plate thickness t, and the like, and the basic mechanical property parameters influencing the fracture resistance are defined by establishing the correlation between the large-size fracture resistance test and the small-size test, the direction is indicated by further regulation and optimization of the fracture resistance, and the development of the domestic fracture resistance steel is greatly promoted.
CN115511167a discloses that the initial value of the crack-stopping toughness and the charpy impact power of the crack-stopping toughness is determined by using a supercritical carbon dioxide pipeline crack-stopping toughness prediction model, whether the initial value meets the crack-stopping requirement is verified by using DNVGL-RP-F104 (2021) crack-stopping acceptance requirement, and the corrected value of the crack-stopping toughness and the charpy impact power of the supercritical carbon dioxide pipeline is obtained, on the basis, whether the corrected value meets the pipeline crack-stopping requirement is verified again by means of finite element simulation, and the final value of the crack-stopping toughness and the charpy impact power of the supercritical carbon dioxide pipeline is obtained, and effective guidance is provided for the crack-stopping design of the supercritical carbon dioxide pipeline. However, the crack-arresting toughness value is obtained by calculation based on the pipeline size parameter, the pipe strength parameter and the calculated supercritical carbon dioxide saturation pressure, and the problems of multiple parameters, complex calculation process, high requirement on test equipment and high test cost exist.
The results of a large number of researches show that the crack-stopping toughness of the crack-stopping thickness has close relation with the impact energy ductile-brittle transition characteristic temperature, the plastic-free transition temperature and the like of the material. The initiation work refers to the energy required to initiate a crack from a crack-free state to the initiation of the crack in the steel. This parameter is of great importance in the field of material fracture mechanics, as it reflects the ability of a material to resist crack initiation. However, at present, no public report is made on the influence of the cracking work of the high-strength cracking-resistant steel on the cracking resistance and the research of a prediction model.
Disclosure of Invention
In view of the above, the invention aims to provide a prediction model for crack-stopping toughness based on the ductile-brittle transition temperature of the crack-stopping steel, so as to solve the problems of complex sample preparation, high requirement on test equipment, complex stress state and high cost of a large-size sample in the prior art.
For the crack-stopping toughness, the use of the method mainly depends on experience and data accumulation, although Japanese class society provides an index of-10 ℃ crack-stopping toughness K ca>6000N/mm3/2 for high-strength steel with 390MPa grade applied to large container ships, whether the index is reliable or not lacks reasonable theoretical basis until now, from the test result of AH36, the crack-stopping toughness value 5829N/mm 3/2 of-10 ℃ is very little different from the index value 6000N/mm 3/2, and the crack-stopping toughness is judged by the crack-stopping toughness, and the test value is 3.6R and is far higher than the preset minimum service temperature-10 ℃, so that the requirement can not be met. In addition, from the point of view of fracture mechanics, the fracture toughness should be applicable to both isothermal type tests and ladder temperature tests, but it is specified that the ladder temperature test can only be used today, and no convincing theoretical explanation is given.
The crack-stopping toughness is used as a physical quantity for representing the crack-stopping performance of the material, the prediction of the crack-stopping toughness is mainly influenced by temperature, crack length measurement precision and fitting precision, and the application scene is focused on scientific research design links, so that the materials can be selected by designers better conveniently.
The determination of the fracture toughness in the prior art depends on a large amount of basic test data, and has the problems of complex sample preparation, high requirement on test equipment, complex stress state and high cost of large-size samples. In order to solve the problem, the invention discloses a novel crack-stopping toughness prediction method, which is based on a small amount of basic test data, and can obtain the association relation between the crack initiation function and the crack-stopping toughness by fitting a selected calculation formula, so that a design tester can conveniently and rapidly determine the crack-stopping toughness of a material, and the test cost is reduced.
In the fitting process, a plurality of calculation formulas are fitted based on a small amount of test data, and the formulas disclosed by the invention are finally selected through comparison of the plurality of data, so that the formulas have higher prediction precision compared with other companies, and the requirements of actual test material selection can be met.
The technical scheme of the invention is realized by a prediction model for crack-stopping toughness based on the ductile-brittle transition temperature of the crack-stopping steel, which comprises the following specific steps:
s1, taking an impact sample in the thickness direction of a high-strength crack-arrest steel plate;
s2, performing a series of temperature oscillometric impact tests on the sample;
S3, extracting the cracking work at different temperatures to obtain a cracking work ductile-brittle transition characteristic curve and a cracking work ductile-brittle transition temperature K a;
S4, performing a double tensile test to measure the crack-stopping toughness K ca of the high-strength crack-stopping steel;
S5, fitting by using a cracking work ductile-brittle transition temperature K a and a cracking resistance toughness K ca to obtain a formula 1:K ca=A+B*Ka;
S6, introducing the cracking work ductile-brittle transition temperature K a into a formula 1 to obtain the corresponding high-strength steel cracking resistance toughness K ca.
Further, in step S1, the high strength crack-stopper steel sheet has a steel grade EH40, EH47 or EH50, a sheet thickness in the range of 50-100mm, and is sampled in 1/4 and 1/2 sheet thickness directions.
Further, in step S2, a series of temperature oscillometric impact tests are performed according to standard GB/T19748, and data recorded during the impact process include test temperature and initiation work KV 2.
Further, in step S3, equation 2:p=is obtained from the relationship between the crack initiation power KV 2 and the crack initiation power ductile-brittle transition temperature k of the sample;
Wherein, P is the slope of the ductile-brittle transition curve;
E Upper platform , a cracking work upper platform in a cracking work ductile-brittle transition curve;
e Lower platform , a cracking power lower platform in a cracking power ductile-brittle transition curve;
x is the temperature.
Further, in step S3, the calculation formula 3:K a=（k1+k2)/2 of the cracking work ductile-brittle transition temperature K a of the crack-arrest steel plate;
wherein k 1 is 1/4 of the ductile-brittle transition temperature of the cracking work in the plate thickness direction;
k 2 is 1/2 of the ductile-brittle transition temperature of the cracking work in the plate thickness direction.
Further, the cracking work ductile-brittle transition temperature K a is in the range of-100 ℃ to-65 ℃.
Further, in step S4, a double tensile test is performed according to standard Q725-1181, the double tensile test is performed at least twice, and the temperature and loading force of the test are recorded.
Further, in step S4, the double tensile test is performed four times at a temperature ranging from-45 ℃ to 0 ℃.
Further, in step S5, the values of the parameters k 1 and k 2 are not less than two when fitting the formula 1.
Further, the values of the parameters k 1 and k 2 are 11, and the range of values is-100 ℃ to 50 ℃.
Compared with the prior art, the prediction model for the crack-stopping toughness based on the ductile-brittle transition temperature of the crack-stopping steel has the following advantages:
1. The method can simply and effectively predict the crack-stopping toughness of the high-strength crack-stopping steel, utilizes the cracking work to obtain the ductile-brittle transition temperature through a small amount of basic tests, does not need to carry out a large amount of double tensile tests, saves test time and cost, has the characteristics of simplicity and high efficiency, and provides technical support for the crack-stopping performance research of the high-strength crack-stopping steel.
2. The invention establishes a correlation model of the average value of the ductile-brittle transition temperature of the cracking work and the crack-stopping toughness K ca of the crack-stopping steel plate in the 1/4 and 1/2 thickness direction oscillographic impact process of the high-strength crack-stopping thick plate from the correlation of the ductile-brittle transition temperature of the cracking work and the crack-stopping toughness of the crack-stopping steel plate in the 1/4 and 1/2 thickness direction oscillographic impact process.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention. In the drawings:
FIG. 1 shows a characteristic curve of ductile-brittle transition of initiation work and ductile-brittle transition temperature of initiation work in the invention;
FIG. 2 shows the crack-arrest toughness K ca of the high-strength crack-arrest steel measured by a double tensile test in the invention;
FIG. 3 shows the correlation between the 1/4 plate thickness direction cracking work ductile-brittle transition temperature K1 and the crack arrest toughness K ca;
FIG. 4 shows the correlation between the 1/2 plate thickness direction cracking work ductile-brittle transition temperature K2 and the crack arrest toughness K ca;
FIG. 5 shows the correlation between the fracture initiation toughness and the brittle transition temperature K a and the fracture stopping toughness K ca in the invention;
FIG. 6 shows a comparison of predicted values of a predicted model of the fracture stopping toughness K ca of the present invention with measured values;
reference numerals illustrate:
Detailed Description
In order to facilitate understanding of the technical means, objects and effects of the present invention, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
It should be noted that all terms such as "upper", "lower", "left", "right", "front", "rear", "vertical", "horizontal", "inner", "outer", "top", "low", "lateral", "longitudinal", "center", etc. used in the present invention are merely used to explain the relative positional relationship, connection, etc. between the components in a specific state, and are merely used for convenience of describing the present invention, and do not require that the present invention must be constructed and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the description of "first," "second," etc. in this disclosure is for descriptive purposes only and is not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated.
In the description of the present invention, unless explicitly stated and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected, mechanically connected, directly connected, indirectly connected via an intermediate medium, or communicating between the two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The invention discloses a prediction model for crack-arrest toughness based on the ductile-brittle transition temperature of crack-arrest steel, which comprises the following specific steps:
s1, taking an impact sample in the thickness direction of a high-strength crack-arrest steel plate;
s2, performing a series of temperature oscillometric impact tests on the sample;
S3, extracting the cracking work at different temperatures to obtain a cracking work ductile-brittle transition characteristic curve and a cracking work ductile-brittle transition temperature K a;
S4, performing a double tensile test to measure the crack-stopping toughness K ca of the high-strength crack-stopping steel;
S5, fitting by using a cracking work ductile-brittle transition temperature K a and a cracking resistance toughness K ca to obtain a formula 1:K ca=A+B*Ka;
S6, introducing the cracking work ductile-brittle transition temperature K a into a formula 1 to obtain the corresponding high-strength steel cracking resistance toughness K ca.
Sampling in the thickness direction of the crack-arrest steel plate to perform a series of temperature oscillography impact tests so as to obtain a crack-initiation ductile-brittle transition characteristic curve and a crack-initiation ductile-brittle transition temperature K a, then performing a small amount of double tensile tests to obtain crack-arrest toughness data, and establishing a relation model of the crack-initiation ductile-brittle transition temperature K a and the crack-arrest toughness K ca, thereby realizing the purpose of predicting the crack-arrest toughness of the crack-arrest steel plate by the crack-initiation ductile-brittle transition temperature.
Compared with the traditional test method, the device has the advantages that only a small amount of basic tests are needed, the crack-stopping toughness can be rapidly predicted through a formula, the test period is greatly shortened, the test cost is reduced, the working efficiency is improved, the device has the characteristics of simplicity and high efficiency, and technical support is provided for the crack-stopping performance research of the high-strength crack-stopping steel.
Specifically, in the formula 1:K ca=A+B*Ka, a and B are coefficients of the formula 1, and values of the coefficients a and B can be obtained after fitting by using the cracking ductile-brittle transition temperature K a and the cracking resistance toughness K ca.
Specifically, in step S1, the high-strength crack-stopper steel sheet has a steel grade EH40, EH47 or EH50, a thickness in the range of 50-100mm, and is sampled in the 1/4 and 1/2 thickness directions.
The crack-arresting steel is mainly applied to the positions of the hatch coaming plate, the web plate, the upper deck, the topboard, the longitudinal bones of the torsion box, the torsion box deck and the like of the ultra-large container ship, where the stress and the alternating load strength are the greatest, so that the steel plate is required to have high strength, high low-temperature toughness, high stress, high crack-arresting property, good welding performance, processability and the like. High strength and high thickness steel plates are commonly used for container ship hulls. The high-strength and large-thickness steel plate can meet the performance requirements, and meanwhile, the stress state of the steel plate is changed from a plane stress state to a plane strain state, so that the cracking resistance of the material is reduced. Through selecting the high-strength crack-arrest steel of the thick plate, sampling is carried out at 1/4 and 1/2 of the thickness direction, the representativeness of the test is ensured, and the performance difference of the steel plate at different thickness positions can be reflected. The high-strength crack-arrest steel grade in China is EH40, EH47 or EH50 generally at present, and the method can cover crack-arrest toughness prediction in the range, and test results can be obtained rapidly through fewer tests.
The sampling requirements of the specific positions are set for testing, the test results of the positions can be compared, the crack arrest performance difference of the steel plate at different positions is known, a basis is provided for the application and design of materials, the crack arrest performance of the steel plate when the steel plate is subjected to impact load is better evaluated, and the performance of the steel plate in practical application is ensured to meet the requirements.
Preferably, when the plate thickness of the high-strength crack-arrest steel is 80mm, the sample is processed into a round bar sample with a gauge length of 50mm and a diameter of 14 mm.
The set sampling requirement can better acquire the performance characteristics of the whole steel plate, meet the test processing requirement, reduce the test size error, eliminate the test result deviation caused by the test sample size error, and improve the accuracy and comparability of test data.
Specifically, in step S2, a series of temperature oscillometric impact tests are performed according to standard GB/T19748, and the data recorded during the impact process include test temperature and initiation power KV 2.
The set test standard can better control the test, reduce errors in the test process and improve the test precision, and the test sample is subjected to the oscillography impact test at a series of temperatures, so that the change of the initiation work at different temperatures is obtained by changing the test temperature, the initiation work and the test temperature schematic diagram are conveniently drawn, and the subsequent fitting of the relationship between the initiation work and the initiation work ductile-brittle transition temperature is facilitated.
Preferably, in step S2, a series of temperature oscillometric impact tests are performed 8 times, the temperature range being-240 ℃ to 0 ℃.
The setting temperature range can cover various stages of high-strength crack-arrest steel fracture, ensure that enough test data are obtained through an oscillography impact test to obtain the ductile-brittle transition temperature of the cracking work, and the test times are set to 8 times, so that the fracture test at each stage has enough test data, the problem that the performance evaluation of the material is influenced by single test data abnormality is avoided, the test error is reduced, and the test accuracy is improved.
Specifically, in step S3, equation 2:p=is obtained from the relationship between the crack initiation power KV 2 of the sample and the crack initiation power ductile-brittle transition temperature k;
Wherein, P is the slope of the ductile-brittle transition curve;
E Upper platform , a cracking work upper platform in a cracking work ductile-brittle transition curve;
e Lower platform , a cracking power lower platform in a cracking power ductile-brittle transition curve;
x is the temperature.
The cracking work ductile-brittle transition temperatures k 1 and k 2,E Upper platform 、E Lower platform at the positions 1/4 and 1/2 of the thickness direction of the steel plate can be calculated through the formula 2 and the cracking function, and the P and x can be quickly obtained from a small amount of test data through fitting.
The setting utilizes the data obtained by a small amount of basic tests, obtains the ductile-brittle transition temperatures k 1 and k 2 of the cracking work according to the formula 1 when different cracking works are performed, avoids obtaining material performance parameters by a large amount of tests, and is beneficial to saving time and reducing cost.
Specifically, in step S3, the calculation formula 3:K a=（k1+k2)/2 of the cracking work ductile-brittle transition temperature K a of the crack-arrest steel plate;
wherein k 1 is 1/4 of the ductile-brittle transition temperature of the cracking work in the plate thickness direction;
k 2 is 1/2 of the ductile-brittle transition temperature of the cracking work in the plate thickness direction.
The cracking work ductile-brittle transition temperature K a of the high-strength crack-arrest steel is obtained by calculating the average value of the sum of the cracking work ductile-brittle transition temperatures at 1/4 and 1/2 of the thickness direction of the steel plate.
The setting can more comprehensively reflect the toughness transformation characteristic of the crack-arresting steel plate in the whole thickness range, is beneficial to more accurately evaluating the overall performance of the crack, reduces errors existing in separately measuring the ductile-brittle transformation temperature of the cracking work at a certain position, and improves the accuracy of evaluation.
Preferably, the cracking work ductile-brittle transition temperature K a is in the range of-100 ℃ to-65 ℃.
The set cracking-work ductile-brittle transition temperature K a test material can meet the equipment requirement in a low-temperature environment, so that the material is suitable for the practical application of high-strength crack-arrest steel, and meanwhile, the model prediction accuracy is higher in the range.
Specifically, in step S4, a double tensile test is performed according to standard Q725-1181.
The set test standard can better control the test, reduce errors in the test process and improve the test precision, and the test sample is subjected to the oscillography impact test at a series of temperatures, so that the change of the initiation work at different temperatures is obtained by changing the test temperature, the initiation work and the test temperature schematic diagram are conveniently drawn, and the subsequent fitting of the relationship between the initiation work and the initiation work ductile-brittle transition temperature is facilitated.
Specifically, in step S4, the double tensile test is performed at least twice, and the temperature and loading force of the test are recorded.
Through repeated identical test conditions, more data points can be collected, the repeatability of the test is verified, accidental errors possibly caused by a single test are reduced, different crack-stopping toughness of the material under different loads is obtained, the relation between different loads and the crack-stopping toughness of the material is obtained by fitting, the method is better used for mechanical property evaluation of the material, and the crack-stopping toughness is rapidly obtained.
Preferably, the double tensile test is performed four times at a temperature in the range of-45 ℃ to 0 ℃.
The accurate crack-stopping toughness of the test material is obtained through four double tensile tests, the influence of too few test times and too large single errors on test results is avoided, curves between the crack-stopping toughness and loads are conveniently obtained, the temperature range is selected from the practical application range of the double tensile tests, and the mechanical properties of the test material in the use process can be better tested.
The setting makes the dual tensile test only need to carry out the test of less times and can obtain the comparatively accurate mechanical properties of material, has significantly reduced the test number of times, saves test time, reduces test cost.
Specifically, in step S5, the values of the parameters k 1 and k 2 are not less than two when fitting the formula 1.
And obtaining the crack initiation toughness and the crack initiation toughness transition temperature at 1/4 and 1/2 positions of the thickness direction of the test material through at least two groups of test data, so as to obtain the association relation between the crack initiation toughness and brittleness transition temperature, further realizing the prediction and evaluation of the crack initiation toughness of the crack initiation thick plate by using the crack initiation, and providing a technical basis for evaluating the crack initiation toughness of the crack initiation thick plate.
Preferably, the values of the parameters k 1 and k 2 are 11, and the range of values is-100 ℃ to 50 ℃.
The method has the advantages that multiple groups of test data are arranged, the problem that the test results are influenced by too few test times and too large single error is avoided, the test accuracy is improved, the association relationship between the crack arrest toughness and the crack initiation toughness-brittle transition temperature can be better fitted, and the prediction accuracy of the model is improved.
Specifically, the predicted relative deviation of the crack-stopping toughness K ca prediction model based on the average value of the crack-starting toughness and brittleness transition temperatures in the plate thickness directions of 1/4 and 1/2 is not more than 11%.
The relative deviation between the crack-arresting toughness K ca and the measured value obtained by using the prediction model can be used for judging whether abnormal conditions occur in the test process, such as errors caused by operation, errors caused by test processing or defects of a sample, and the like, and a group of data can be reserved in a double tensile test to be used for checking whether the test result is correct or not, so that the test accuracy is improved.
The device can verify the accuracy of the test process, avoid the interference of the test result due to the error of the sample or the test process, and improve the reliability of the test result.
Example 1
1. Sampling the high-strength crack-arrest steel plates of different batches in the 1/4 and 1/2 thickness directions according to GB/T19748 'method for instrumented test of Charpy V-shaped notch pendulum impact test for metal materials', carrying out oscillography impact test to obtain the crack initiation work at different temperatures, calculating the crack initiation work ductile-brittle transition temperature according to formula 2 as shown in figure 1, calculating the crack initiation work ductile-brittle transition temperature average value K a in the 1/4 and 1/2 directions according to formula 3, and carrying out double tensile test on the high-strength crack-arrest steel plates of different batches according to Q725-1181 as shown in figure 2 to obtain the crack-arrest toughness K ca.
Table 1 1/4 and 1/2 plate thickness directions cracking work toughness and brittle transition temperature and crack arrest toughness
2. Substituting the data in table 1 into formula 2, performing linear fitting, as shown in fig. 3-5, and obtaining undetermined parameters as shown in table 2, wherein the form of the prediction model is shown in formula 4. The predicted value and the measured value of the crack-arrest toughness K ca are shown in FIG. 6, and the predicted value and the measured value of the crack-arrest toughness K ca are shown in Table 3. The relative deviation of the prediction model prediction of the crack-stopping toughness K ca based on the average value of the crack-starting toughness and brittleness transition temperatures in the 1/4 and 1/2 plate thickness directions is not more than 11%.
Table 2 calculation of the values of the parameters to be determined in the model
Formula 4:K ca=A+B*Ka
TABLE 3 predicted and measured values of crack arrest toughness K ca based on the average of the crack initiation work ductile-brittle transition temperatures in the 1/4 and 1/2 plate thickness directions
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
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