Some observations on failure of austenitic stainless steel: effects of in- and out of plane constraint

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Procedia Structural Integrity 18 (2019) 457–471

25th International Conference on Fracture and Structural Integrity 25th International Conference on Fracture and Structural Integrity

Some observations on failure of austenitic stainless steel: effects of Some observations on failure of austenitic stainless steel: effects of in- and out of plane constraint in- and out of plane constraint Mehdi Mokhtarishirazabad*, Mahmoud Mostafavi Mehdi Mokhtarishirazabad*, Mahmoud Mostafavi Department of Mechanical Engineering, University of Bristol, Bristol, UK Department of Mechanical Engineering, University of Bristol, Bristol, UK

Abstract Abstract Modern engineering design for safety-critical structures demands meticulous failure assessments. While conventional fracture Modern structures demands failure the assessments. While conventional fracture or safety-critical KIC) are perceived as a reliable tool meticulous for characterizing fracture behaviour of many engineering toughnessengineering parameters design (e.g. JICfor ) are perceived as a reliable tool for characterizing the fracture behaviour of many engineering toughness parameters JIC or K components, excessive(e.g. plasticity inIClow-strength materials with high strain hardening capability, such as austenitic stainless steels, components, excessive plasticity in low-strength materials with strainassessing hardening such as austenitic stainless steels, can change the predominant failure mode to plastic collapse. In high this case, thecapability, component integrity assuming fracture can can change the predominant failure mode to plastic collapse. In this case, assessing the component integrity assuming fracture can introduce significant conservatism in its estimated load bearing capacity. Low constraint structures such as thin sections or sections introduce in its collapse estimatedrather load bearing capacity. Low is constraint structures suchpredict as thinthe sections with shortsignificant cracks can conservatism suffer from plastic than fracture but there not a measure that can changeorofsections failure with short cracks canstudy, sufferthe from plastic collapse than in fracture there is not a measure that can size predict change of failure mechanism. In this effect of crack tip rather constraint terms but of the thickness and initial crack on the failure behaviour of mechanism. In thisaustenitic study, the effect ofsteel crack constraint in terms of the thickness andnotched initial crack size(SENB) on failure behaviour of AISI Type 316L stainless is tip studied. To this end, several single edge bending specimen were AISI Type 316L austenitic stainless steel is studied. To this end, several single edge notched bending (SENB) specimen were manufactured with different initial crack lengths and thicknesses to account for in- (i.e. crack length) and out of (i.e. thickness) manufactured with different initial lengthsaccording and thicknesses to account forexcept in- (i.e. length)thickness and out and of (i.e. thickness) plane constraint effect. Fracture testscrack performed to ASTM E1820-18 forcrack the sample crack lengths. plane constraintfor effect. Fracture to ASTM E1820-18 the sample thickness and crack lengths. The challenges measuring thetests crackperformed extensionaccording for resistance curve method as aexcept result for of deviating from the standard is discussed. The forsamples measuring extension for resistance curve method(FAD). as a result deviating fromthat theunloading standard iscompliance discussed. The challenges failure of the wasthe alsocrack assessed by Failure Assessment Diagram Theofresults showed The failureunderestimate of the samples the wascrack also assessed byinFailure Assessment Diagram (FAD). results showed unloading extremely extension the presence of significant plastic The deformation of the that samples. The compliance results also extremely the crack extension in the presence of significant plastic deformation of the samples. The results also showed thatunderestimate the plastic collapse occurs in all samples before crack starts to grow, in the blunting regime. showed that the plastic collapse occurs in all samples before crack starts to grow, in the blunting regime. © 2019 The Authors. Published by Elsevier B.V. © 2019 Published by Elsevier B.V. B.V. © 2019The TheAuthors. Authors. Published by Peer-review under responsibility of Elsevier the Gruppo Italiano Frattura (IGF) ExCo. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Keywords: Austenitic stainless steel; fracture toughness; in-plane constraint; out of plane constraint; plastic collapse Keywords: Austenitic stainless steel; fracture toughness; in-plane constraint; out of plane constraint; plastic collapse

* Corresponding author. Tel.: +44 7746872877. * Corresponding Tel.: +44 7746872877. E-mail address:author. [email protected] E-mail address: [email protected] 2452-3216 © 2019 The Authors. Published by Elsevier B.V. 2452-3216 2019responsibility The Authors. of Published by Elsevier Peer-review©under the Gruppo Italiano B.V. Frattura (IGF) ExCo. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo.

2452-3216  2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. 10.1016/j.prostr.2019.08.188

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1. Introduction Fracture behaviour of stainless steel in plane strain condition is well established. This includes substantial studies on the effect of in-plane constraint (Picker 1983; Mills 1997; Ruggieri 2017; Hioe et al. 2017). Conversely, there only have been few studies of the fracture behaviour of stainless steel alloys with low out-of-plane constraint. This is because the majority of safety critical components have thick sections. However, there are components, such as thin tubes in heat exchangers, which may be subject to both a loss of in-plane and out-of-plane constraint. The thin components, which are believed to be more susceptible to plastic collapse when as-manufactured, can become prone to fracture after thermal ageing. Therefore, alternative approaches to assessing the integrity of thin components are required. The standard fracture toughness values according to standard methods such as ASTM E1820 are measured with the condition of high in-plane and out-of-plane constraints. However, this condition does not always apply to service components. There are studies which used the standard methods but did not follow the prescription on minimum crack length, for example, to evaluate the effects of loss of in- and out-of-plane constraint (Zhu 2016). We adopted the same approach to study the effects of loss of out-plane constraint. 2. Methodology The tensile properties of the material were evaluated by performing tensile tests on three flat dog-bone samples extracted from the middle of the plate with thickness of 5 mm, following the ASTM standard (ASTM-E8/E8M 2016). Fig. 1 shows the geometry of the tensile test sample. The loading for tensile tests was applied by an Instron 5969 Universal testing machine with a load cell capacity of 50 kN, under displacement control with a loading rate of 0.5 mm/min. All tensile experiments have been conducted with the same equipment and testing parameters in a single day.

Fig. 1. Geometry and dimensions of the tensile test sample.

Fracture experiments were carried out on plane sided SENB samples made of austenitic stainless steel 316L. The samples were machined in a way that the direction normal to the crack plane was parallel to the rolling direction while crack propagation direction was perpendicular to the rolling direction (LT direction). Side grooving was avoided to be able to have a full field displacement measurement near the crack tip area by employing 3D digital image correlation (DIC) method. Full-field measurements by DIC are under study and will be published separately. In this paper only some examples of the images taken from the crack region during loading are presented. The width of these samples was 50 mm. To study the effect of in plane and out of plane constraint, samples with four different initial crack lengths of a/W = 0.2, 0.3, 0.4 and 0.5 and three different thickness of 5, 10, 20 mm were machined, respectively. In addition, one CT samples were machined with thickness of 20 mm and a/W = 0.5. Therefore, 14 SENB samples and 1 CT samples were made in total (Table 1). Fig. 1 shows the geometry and dimensions of the specimens. Wire EDM was used to introduce initial cracks as previous research showed that considerable crack blunting prior to growth eliminates the effect of fatigue pre-crack (Mostafavi, Smith, and Pavier 2010). The dimensions of the specimens are provided in Table 1. A 3-point bending stage with rolling supports was used to carry out SENB tests. For the thinnest samples (thickness of 5 mm), anti-buckling plates were used (see Fig. 3). A sample naming convention SENB_BX_Y was adopted in which X is the sample thickness in mm and Y is a/W.



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Table. 1. The list of the plane-sided samples Dimensions Geometry

Sample code

CT

CT-B20_0.5 SENB_B20_0.5, × 3 SENB_B20_0.4 SENB_B20_0.3 SENB_B20_0.2 SENB_B10_0.5 SENB_B10_0.4 SENB_B10_0.3 SENB_B10_0.2 SENB_B05_0.5 SENB_B05_0.3 SENB_B05_0.2

SENB

W (width, mm)

B (thickness, mm)

S (support distance, mm)

a_ini, (initial crack length, mm)

50.06 50 50.05 50.01 50.04 49.90 49.886 49.9 49.92 49.99 50.03 49.93

20.78 20 20.77 20.77 20.75 9.64 9.65 9.65 9.64 4.986 5.02 5.005

200 200 200 200 200 200 200 200 200 200 200

24.93 25 20.12 15.14 10.01 25.12 20.125 15.12 10.13 25.00 15.13 10.04

Fig. 2. Geometry and dimensions of the (a) SENB and (b) CT specimens. Dimensions are in mm.

Fig. 3. The anti-buckling jig designed for fixing the SENB samples with thickness of 5 mm.

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The compliance method was used to measure the crack length during the tests and to compare with values observed by DIC on the surface of the samples. Since the total crack mouth opening displacements in non-standard specimens were higher than the maximum travel range of the available crack mouth opening displacement (CMOD) gauges, a video extensometer (iMetrum Ltd) was used. The load was applied by a hydraulic Instron 1342 testing frame with a 250 kN capacity equipped with a load cell of the same capacity. Samples at the extreme end of each condition were heat tinted at 450 ºC for 30 minutes and then broken open to measure the physical crack length (Δap) and study the fracture surface. Full-field displacement around the crack tip was measured using a 3D Digital Image Correlation (DIC) system (LaVision Ltd). Images with 2254 × 2054 pixels resolution were captured over the duration of the test. LaVision cameras with 5 MP CCD and 12 bit depth and Tokina 100mm F2.8 Macro lenses with a working distance of 800 mm were used. Field of view (FOV) 47 × 38 mm2 was obtained. In order to provide imaging contrast, a fine speckle pattern was applied to the surface of the specimens using spray paint. The setup of test equipment and an example of the obtained images are shown in Fig.4. Image post-processing was done by Davis version 8.4.0 to extract the fullfield displacement around the crack tip. The results of DIC analysis will be presented in a separate work.

Fig. 4. (a) the setup of the 3D DIC equipment and (b) the acquired image of the surface of the sample.

3. Results and Discussion 3.1. Tensile properties Table 2 shows the results of the tensile tests on 316L stainless steel alloy used in this study. An extraordinary strain hardening capacity was observed. That is the ratio of σuts over σys was about 2.5 while the elongation at maximum load was around 50%. In addition, the elongation at fracture was about 80%. An average of the tensile properties of these samples was used in this study. Table 2. Tensile properties of the 316L stainless steel Sample

σys(0.2% offset), MPa

σUTS, MPa

Elongation after Fracture, %

E, GPa

TT-1 TT-2 TT-3

249 249 245

611 609 609

82 81 83

207 202

3.2. Fracture of CT specimen Fig. 5 shows a CT sample after the standard loading sequence is completed. Visual inspection showed that the uncracked ligament of the specimen had plastically deformed. It was also observed that the pin-holes had visibly deformed. Both these conditions invalidate the evaluations of fracture toughness by ASTM, therefore testing the CT samples was not completed. The possibility of specimen failure by plastic collapse was considered in the analysis. Failure of plane-sided CT specimen by plastic collapse has been previously reported by Wasylyk et al. (Wasylyk and Sherry 2010).



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Fig. 5. CT specimen deformation during the test. Plastically deformed areas are marked by dashed lines.

3.3. Fracture of plane sided SENB specimen Fig. 10 shows the sequences of sample surface deformation from zero load to maximum load for SENB_B20_0.5_3. Significant crack tip blunting can be seen before stable tearing at the tip of EDM slit occurs. Such blunting behaviour suggests that a 0.1 mm EDM notch can work like a fatigue pre-crack, eliminating the timeconsuming stage of sample preparation.

Fig. 6. Extensive crack tip blunting before crack propagation at the surface of the SENB_B20_0.5 sample.

The load as a function of the CMOD for samples with thicknesses of 5, 10 and 20 mm with the a/W = 0.5 and 0.2 are shown in Fig. 7. It can be seen that the maximum load for samples with shorter crack length was higher than larger cracks while CMOD is less for samples with shorter cracks rather larger cracks at maximum load. For all specimens, the resistance curve was plotted following ASTM standard. It worth noting that the ASTM equation for plotting the blunting line is valid for most materials. However, in case of low strength materials with high strain hardening capability such as austenitic stainless steels, using this equation leads to overestimating the fracture toughness of the material (Mills 1997). To address this issue, the theoretical blunting line is plotted using the following equation (Landes 1995):

𝐽𝐽 � � � ���� � �� 

where M = 3.75 for stainless steel 316 (Landes 1995) and σuts is the ultimate tensile strength of the material.

(1) 

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Fig. 8, shows the R-curve of the three SENB_B20_0.5 samples; all samples had the same geometry and dimensions. A significant discrepancy in the measured crack extension by unloading compliance (UC), ΔaUC was observed. However, Fig. 9 shows that the loading sequences and response of the samples were very similar. The scatter is due to variation in the UC in the load-CMOD graphs of the same geometry. In Fig. 9, sample SENB_B20_0.5_01 differs slightly to the other two specimens. This sample was tested at a higher rate and larger displacement intervals. Room temperature rate dependency has been observed in stainless steel 316L and have been attributed to cold creep (Moreton and Sellings 1989); the initial part of the curve is much steeper than the theoretical blunting line in the plot, which can be attributed to the underestimation of the crack length measured by UC.

Fig. 7. The graph of load as a function of CMOD for samples with thicknesses of 5, 10 and 20 mm and a/W = 0.5 and 0.2.

Fig. 8. R-Curve for SENB_B20_0.5 samples.



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Fig. 9. Force as a function of CMOD for SENB_B20_0.5 samples showing similar responses for sample number 02 and 03. Sample 01 was tested at higher displacement rate and larger displacement intervals.

The effect of initial crack length on crack growth resistance of the samples with the thickness B = 20, 10 and 5 mm is illustrated in Fig.10. The standard procedure for converting JQ to J0.2 is not valid for these specimens, where J0.2 refers the fracture toughness at 0.2 mm offset form blunting line. Nonetheless, it can be seen that by decreasing the initial crack length (smaller value of a/W; low in-plane constraint), the critical energy for crack extension is decreased. This finding is in contrast with expected fracture behaviour of ductile materials in tensile type (mode I) fracture and therefore suggests shear type (mode II) fracture is the failure mechanism.

Fig. 10. Fracture surface of plane-sided samples with different thicknesses. Different regions in the fracture surface are marked in the image. Table 3. Measured crack extension by UC (ΔaUC) and fracture surface (Δap) and estimated values of JQ for samples with the thickness of 10 mm and 5 mm.

0.5

ΔaUC, mm 0.745

Δap, mm 3.461

Error in estimation of Δa, % 365

JQ (kJ/m2) -

0.2

2.592

4.831

86

3651

0.5

2.944

4.877

65

3072

10

0.2

4.110

5.013

22

2489

SENB_B05_0.5

5

0.5

3.833

5.439

42

1697

SENB_B05_0.2

5

0.2

6.614

7.063

7

1288

Sample

a/W

SENB_B20_0.5

Thickness (mm) 20

SENB_B20_0.2

20

SENB_B10_0.5

10

SENB_B10_0.2

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These samples were heat tinted and broken open to measure the final crack length optically (Fig. 10). Crack length measurement was conducted following ASTM 1820 standard, although the requirements for the shape of the crack front was not met. It was observed that significant crack tunnelling had occurred in these samples. A nine-point average procedure based on optical measurement of the crack extension was performed to validate the ΔaUC. The results are reported in Table 3. It was observed that crack extension was significantly underestimated by using the UC method, especially for high constraint samples. It was observed that difference between physical crack extension (Δap) and ΔaUC was alleviated for shorter cracks and thinner samples which have lower in- and out-of-plane constraint; it appears that the UC method is more accurate in this condition. For example, the error in estimating the ΔaUC for samples with thickness of 5 mm and a/W = 0.2 and the sample with thickness of 20 mm and a/W = 0.5 were 7% and 365%, respectively. To explain the higher accuracy of low constraint samples, one should explore the sources of errors in UC method when a ductile material is tested. Two of these sources are the magnitude of deformation and indentation of rollers in the contact area. As it can be seen from Fig. 9, by decreasing the initial crack length, the maximum CMOD (maximum deformation) for each thickness was almost halved. On the other hand, by decreasing the thickness, the samples went under lower loads. That is, by dividing the maximum load by the thickness of each sample (117 kN, 55 kN, and 26 kN divided by 20, 10 and 5 mm, respectively), it can be seen that the ratio also reduced from 5.85 to 5.2 from thickest to thinnest sample. This means that we applied lower load per unit of thickness in thinner samples, and as a result, lower indentation deformation in contact areas. Both factors (specimen deformation and indentation of the rollers) are perceived as sources of error for underestimating the crack length by UC (Steenkamp 1988). Therefore, reduction of these factors in low constraint samples, can be perceived as the reason for better estimation of the crack extension. The significant underestimation of crack extension can be the reason for unusual fracture behaviour in relation to loss of in- and out-of-plane constraint. Therefore, to evaluate a valid fracture toughness value for the samples being studied, it is essential to have an accurate and reliable estimation of the crack extension. Fig. 11b, shows the R-curves for the 10 mm thick samples. It can be seen that there are two regimes of behaviour: crack tip blunting at low extensions (less than 0.9 mm) and stable ductile crack tearing above 0.9 mm (Paris et al. 1979). However, the aforementioned under-prediction of the crack extension by the UC method has led to evaluating a steeper experimental blunting line for these samples. That is, if a line fits to the low crack extension data, it’s slope will be higher than the slop of the blunting line in R-curve (Eq. 1). With respect to 5 mm thick samples, shown in Fig. 11c, there is good agreement between the experimental and theoretical blunting behaviour. Following the ASTM routine for evaluating JQ, it was observed that by increasing the initial crack length, the estimated value of JQ increases for samples with 10 mm and 5 mm thickness (Fig.12). This suggests that the loss of out-of-plane constraint leads to lower crack growth resistance. It should be mentioned that, to obtain a valid J-R curve for 20 mm thick samples, a detailed FE analysis is required for modifying the compliance calibration function when samples experience considerable deformation. More details about the sources of errors when UC is using for crack length measurement at the presence of high deformation is discussed in the next section. Although there seems to be an agreement between the effect of loss of constraint – in-plane and out-of-plane – on the behaviour of stainless steel 316 at room temperature, any interpretation of such trends should be done after correcting the crack extension. In both cases the resistance curve seems to decrease as the constraint decreases (as depicted in Fig. 12). A possible explanation for this behaviour is that the fracture mechanism of the material at this temperature is judged to be shear – in which the von-Mises stress is the dominant contributor. The loss of constraint lowers the stress triaxiality, therefore increasing the share of von-Mises stress compared to that of hydrostatic stress at any given energy level promoting fracture. Fig. 13 shows how the critical stress intensity factor changes by specimen thickness (Adams, Lai and Ferguson 1986). It can be seen that by decreasing the thickness of a specimen, the contribution of shear fracture increases until a critical thickness in which KC hit a pick. Further thickness reduction results in a drop in KC, where pure slant fracture occurs (Anderson 2017; Adams, Lai and Ferguson 1986). It could be argued that, as the material approaches plastic collapse, it becomes more likely that shear type of fracture becomes the dominant failure mechanism.



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Fig. 11. The effect of initial crack length on R-Curve behaviour for SENB samples with the thickness of (a) 20 mm, (b) 10 mm and (c) 5 mm.

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Fig. 12. Effect of thickness (out-of-plane constraint) and crack length (in-plane constraint) on JQ for plane-sided samples. Unexpected trend in JQ can be attributed to erroneous crack extension measurement by UC method.

Fig. 13. Dependence of critical stress intensity factor on specimen thickness (Adams, Lai and Ferguson 1986).

3.4. Correction of ΔaUC Probably the easiest method for tackling under-prediction of ΔaUC is to use a linear scaling method. This can be applied by multiplying ΔaUC to the ratio of measured Δap divided by calculated ΔaUC (Dzugan 2003); J-integral is then calculated based on corrected crack lengths. This method was applied to SENB sample with thickness of 10 mm and a/W = 0.2 and 0.5, with the corresponding graph shown in Fig. 14. Although employing this method resulted in better estimation of final crack extension, it could not address the steeper blunting line of experimental results though. In addition, the value of JQ is still higher for higher constraint condition. The other way to correct ΔaUC is to analyse the effects occurring during the bending of the SENB sample. Fig. 15 shows the sources of errors arising during bending the SENB specimen for measuring the ΔaUC. These factors (Steenkamp 1988; Perez Ipiña and Santarelli 1989; Wallin 2014; Dzugan 2003) include:     

Specimen deformation, Movement of and friction at the outer rollers, Crack front curvature, Roller indentation Effective thickness and Young’s modulus.



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Fig. 14. Effect of applying the linear scaling method for correcting the estimated ΔaUC for SENB samples with thickness of 10 mm and a/W= 0.2 and 0.5.

Steenkamp (Steenkamp 1988) is a comprehensive analytical study on the effect of these factors on compliance measurement on 3-point bending specimens. It reports that deformation of the specimen has the most significant effect on the measurements, while the effect of other factors is approximately 1%. It should be mentioned that, in literature, the effect of these factors has been taken in to account up to a limited amount of plastic deformation (up to 5 mm of plastic deflection) (Dzugan 2003; Steenkamp 1988) while the plastic deflection of more than 10 mm was observed in 316L in this study. To account for sample deflection effect, a correction factor is suggested by Steenkamp, FD, which increases with deflection of the sample. FD is proposed in the following form: 𝐹𝐹𝐹𝐹 � � � ����� � �  ��

∆   ���

(2)

(3)

where α is the deformation angle as defined in Fig. 15 and Δ is the load line displacement. The effective compliance is therefore: 𝐶𝐶� �

𝐶𝐶   𝐹𝐹𝐹𝐹 �𝐹𝐹𝐹𝐹 � �

(4)

where C is the experimental compliance and FD0 is the FD at first unloading increment (fully elastic). In this experiment α was determined directly from the DIC images. Fig. 16 shows that employing the proposed correction by Steenkamp on sample SENB-B10-0.5 and SENB-B05-0.2 does not result in a consistent correction of the crack length measurement for samples with different thicknesses: it underestimates the crack extension in SENB-B10-0.5, whilst overestimating it for SENB-B05-0.2. Nevertheless, employing this method has improved the fitting of experimental and theoretical crack tip blunting. However, a better solution would involve use of a finite element method. This would have to account for large plastic deformation; the compliance estimations would also have to be corrected before UC could be used to estimate the crack length.

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Fig.15. Sources of errors arising in measuring the crack extension by compliance method (after Steenkamp (Steenkamp 1988)).

Fig. 16. Comparing the UC correction methods for measuring the crack extension for (a) samples SENB-B10-0.5 and (b) SENB-B05-0.2.



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3.5. Failure Assessment Diagram The fracture data of the plane-sided samples were analysed using Option 1 in a Failure Assessment Diagram (FAD) (R6: Assessment of the Integrity of Structures Containing Defects). Although using the Option 2, can reduce conservatisms in Option 1, both options result in similar curves for materials with high strain hardening capacity like austenitic stainless steel. The failure assessment line, Kr and Lr are defined as follows: 𝑓𝑓� �𝐿𝐿� � � �� � ���𝐿𝐿� � ����� ���3 � ��� ��������𝐿𝐿�� �� 𝐾𝐾� �

where

𝐿𝐿� �

𝐾𝐾�� ���𝑛𝑛�𝑎𝑎� ��𝑎𝑎�𝑡𝑡�� �𝑡𝑡���� �𝑛𝑛𝑡𝑡�𝑛𝑛��𝑡𝑡� 𝑓𝑓𝑎𝑎�𝑡𝑡��� 𝐾𝐾��� �𝑓𝑓�𝑎𝑎�𝑡𝑡��� 𝑡𝑡����𝑛𝑛����

𝑁𝑁��𝑡𝑡�𝑡𝑡𝑎𝑎��𝑎𝑎������ ��𝑎𝑎� ����𝑛𝑛� ���� 𝑡𝑡� 𝑡𝑡 � �𝑡𝑡������� 𝑁𝑁� ���𝑎𝑎�𝑡𝑡�������𝑡𝑡 ��𝑎𝑎� �𝑓𝑓 𝑡𝑡�� 𝑓𝑓�𝑎𝑎��� �𝑡𝑡���𝑡𝑡��� �

𝑁𝑁� �����𝑡𝑡���𝑎𝑎�� �

(5)

(6)

(7)

𝑛𝑛� 𝑊𝑊 � 𝑡𝑡𝑡𝑡� 𝑎𝑎 2 , 𝑛𝑛� � ��22��� � � � �, � � , � �   2𝑆𝑆 𝑊𝑊 √3

(8)

Kmat is defined as follows (Anderson 2017):

𝐾𝐾��� � �

𝐽𝐽��� � �   �� � � � �

and KI is calculated based on Murakami (Murakami 1987). Here we used JQ (measured after applying linear scale correction for crack extension) as the J0.2. The FAD for samples with a/W = 0.5 and two different thicknesses of 10 mm and 5 mm are shown in Fig. 17. The sample with 20 mm thickness was not plotted due to considerable error in crack extension measurement by UC. Each point in this figure corresponds to the load just before the unloading in the fracture test. The highlighted marks in this figure show the corresponding load at J0.2. The main point of this figure is that the samples failed by plastic collapse much earlier than any crack growth occurred. That is uncracked ligament failed during crack tip blunting. 4. Conclusion The fracture toughness of Stainless Steel 316L has been assessed by ASTM standards, with crack extensions estimated by the compliance method. It has been found that:  The compliance method significantly under-predicted crack extension, particularly for plane-sided thick samples. Two correction methods were used to improve the UC estimation, but both of these resulted in inconsistent estimations by variation of the thickness and initial crack length of samples.  By decreasing the sample thickness (loss of out-of-plane constraint) and the initial crack length (loss of in-plane constraint), the estimated value of JQ also decreases. This was contrary to expectations. The main reason for this observation was the significant underestimation of the crack extension when using compliance method. Therefore, when considerable deformation is expected for fracture test, the equations used in compliance method for samples would need to be modified and validated by a FE analysis.

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 Considerable plastic deformation in the un-cracked ligament of the specimens showed that the failure occurred by plastic collapse in all cases (as shown by fully plastic J and FAD analysis).  Plastic collapse occurred before the cracks start to grow (during the early loading unloading sequences in crack tip blunting regime) These observations suggest that austenitic stainless steel, particularly AISI type 316L, which shows an extraordinary strain hardening capacity is not suitable for studying the constraint effect. Further study is currently in progress to examine the effect of long-term aging treatment on mechanical properties and fracture behaviour of this type of steel.

Fig. 17. Failure Analysis Diagram for samples with thicknesses of 10 mm and 5 mm with a/W=0.5. The highlighted marks show the Lr at J0.2.

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