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A note on the effect of plastic strain on fracture toughness
Pergamon
Engineering Fracture Mechanics Vol. 57, No. 1. pp. 67 73, 1997
PIh S0013-7944(96)00134-8
A NOTE
ON
THE
EFFECT
FRACTURE
OF
~. 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain oo13-7944/97 $17.oo + o.oo
PLASTIC
STRAIN
ON
TOUGHNESS
LESLIE BANKS-SILLS and I N N A D U N Y E The Dreszer Fracture Mechanics Laboratory, Department of Solid Mechanics, Materials and Structures, The Fleischman Faculty of Engineering, Tel Aviv University, 69978 R a m a t Aviv, Israel
Abstract--The fracture
toughness Ktc is employed regularly to predict catastrophic failure of many structures, In this study, experiments are carried out on three-point bend aluminum alloy (AI 7075T7351) specimens. The material from which the specimens are fabricated is subjected to several uniform tensile overloads. The overload causes a constant plastic strain within the material. It is seen that as the overstrain level is increased, the fracture toughness is reduced up to a factor of approximately 20%. A micro-mechanistic model is employed to determine KI~ values from the current yield stress. The trend shown by the model is similar to that determined by the tests. (~) 1997 Elsevier Science Ltd
1. I N T R O D U C T I O N THE FRACTURE toughness Klc is employed regularly to predict catastrophic failure. Well before failure, many structural materials undergo fatigue loads and various overloads such that critical regions are subject to plastic deformation. The effect of prestrain has been examined in the case of steels, in particular, in their application to pressure vessels which undergo proof testing. Several situations are of interest: (1) warm prestressing, (2) an overload applied to a cracked body and (3) an overload applied to an intact body. A review of these subjects is presented in ref. [1]. In this study, the last situation is investigated by testing an aluminum alloy, A1 7075T7351, to determine the effect of permanent deformation on fracture toughness. Some of the results relating to this topic only and reported in the literature for steels are reviewed here; this list is incomplete. In ref. [2], HY-80 low strength steel was subjected to four levels of compressive prestrain. The Klc values were seen to increase by about 12% for prestrains up to 17%, whereas these values began to decrease thereafter by as much as 25% at 56% residual strain. In ref. [3], Jic and critical crack opening displacement values were measured for 316 stainless steel. These values were seen to decrease as the percent of cold rolling increased from zero to 30%; the decrease was more than 60% at the highest prestrain. Mild steel, En32B, was compressed by nominal strains of 10% and 20% [4]. Initiation J values were determined and seen to decrease by as much as 75% depending upon crack orientation. AISI-4340 steel was investigated in refs [5, 6]. Material was prestrained by both cold rolling (compression) and tension. Fracture toughness tests were conducted on specimens machined from this material. The same trends were observed in both cases. The fracture toughness increased as much as 4.6 times its value at the annealed state as the prestrain level increased to 2%. It then decreased until at 10%, it reached a level approximately 25% less than that determined for the annealed material. The effect of two levels of prestrain on the stress intensity level of mild rolled steel was investigated in ref. [7]. Specimens were fabricated from prestrained long rectangular rods. It was found that at two values of the load line displacement, the stress intensity factor decreases for 3% prestrain and increases for 7% prestrain, as compared to virgin material. In ref. [8], HY-100 steel was subjected to prestrains of 5, 6, 8 and 10%. The measured values of Jlc decreased by about 25% at 10% prestrain as compared to material which was not subjected to a prestrain. In this investigation, long aluminum alloy, A1 7075-T7351, specimens are subjected to several tensile overloads creating different levels of plastic deformation with residual stresses minimized. First, the fracture toughness of this material is determined by testing four three-point bend specimens. The results are presented in Section 2. Then, in the form of long dog-bone specimens, the material is subjected to five different tensile overloads. Three-point bend specimens are fabricated from this material which contains permanent deformation or overstrain. Fracture toughness tests are carried out on these specimens. The results which are described in Section 3 67
L. BANKS-SILLS and I. D U N Y E
68
Table I. Chemical composition by percent of AI 7075-T7351 [10] Si
Fe
Cu
Mn
Mg
Cr
Zn
Ti
0.4
0.5
1.2 2.0
0.3
2.1-2.9
0.18-0.28
5.1-6.1
0.2
demonstrate a clear effect on the fracture toughness. In Section 4, a fractographic examination of crack surfaces is presented. A micro-mechanistic model[9] is employed in Section 5 to calculate the fracture toughness and compare with those values determined experimentally. 2. FRACTURE T O U G H N E S S TESTING The aluminum alloy, A1 7075-T7351, of nominal thickness 13 mm has been selected for study. A typical chemical composition is given in Table 1 [10]. Four fracture toughness tests in the T - L direction were carried out with an Instron loading machine (model 1341) on threepoint bend specimens according to ASTM standards[11,12]. Guides were added to the standard Instron three-point bend test fixture which position,s the specimen so that the load could be placed exactly at the span center and the span S is precisely 102 ram. All specimens were precracked from a chevron notch at 10 Hz with R = 0.1. The pre-cracking procedure fulfilled all restrictions imposed by the standard. Specimen measurements and results are presented in Table 2. All test records were of Type I. The largest ratio of Pmax/PQfor these tests was 1.04 which is well within the limitation for a valid Kic test. The 0.2% yield stress in the unstrained condition was found to be 452.2 MPa. According to this, the specimen thickness B and crack length at fracture ac should be at least 18.5 mm when the factor 5 (KiQ/aV) 2 is employed. The minimum factor of 3.5 instead of 5 is obtained with specimen number 002. Although these results coincide with similar results given in the literature for this material[13, 14], none of the results may be considered valid fracture toughness values according to this criterion in ref.[12]. The average value of K I Q is seen to be 27.2 MPax/-m. 3. FRACTURE TOUGHNESS TESTING OF OVERSTRAINED MATERIAL Long dog-bone specimens were fabricated with nominal overall length 630 mm and a gage length of 390 mm. These specimens were subjected to five different tensile overloads perpendicular to the material rolling direction producing a plastic permanent set or overstrain of 0.96, 2.0, 3.2, 3.96 and 5.1%. The tensile overload was induced in an Instron loading machine (model 1250). Before inducing the plastic deformation, the alignment of the load system and specimens were examined according to the ASTM standard E 1012-89115]. Three sets of four strain gages were placed on the specimens at the center of the gage area and equally spaced at 142 mm from the center. The minimum and maximum percent of bending at any of these three positions was 3.3% and 8%, respectively, at an applied load of 78.5 kN. The percent of bending decreases as applied load increases. The dog-bone specimens were subjected to a maximum load of approximately 175 kN. Hence, in the range that the overload is induced, the percent of bending is much less, so that only very small residual stresses are assumed present in the specimens. After the overstrain was induced in each of five dog-bone specimens, three-point bend fracture toughness specimens were fabricated from the gage region. For each dog-bone, three specimens were fabricated. Fracture toughness tests were carried out according to the ASTM standard [11]. The pre-cracks were induced as described in the previous section. In Tables 3-7 the results are presented. All test records were Type I with the maximum value of Pmax/PQ Table 2. Fracture toughness test results for AI 7075-T7351. The yield stress a v = 452.2MPa Specimen 002 003 004 005
B (mm)
W(mm)
a~(mm)
Po(N)
KIQ ( M P a ~ m )
12.94 12.91 12.90 12.95
25.40 25.39 25.40 25.42
13.02 12.98 12.60 12.87
5093.8 4971.9 5312.5 5125.0
27.5 26.8 27.3 27.1
Effect of plastic strain on fracture toughness
69
Table 3. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 0.96%. The maximum stress before unloading is 476.1 MPa Specimen 1.1 1.2 1.3
B (mm)
W (mm)
ac (mm)
PQ (N)
KIQ (MPax/m)
12.87 12.86 12.87
25.21 25.26 25.20
12.73 12.85 12.78
4781.3 4718.8 4656.3
25.6 25.5 25.1
Table 4. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 2.0%. The maximum stress before unloading is 491.1 MPa Specimen 2.1 2.2 2.3
B (mm)
W (mm)
ac (mm)
PQ (N)
KIQ (MPax/m)
12.76 12.78 12.79
25.21 25.25 25.26
12.55 12.68 12.74
4468.8 4468.8 4562.5
23.6 23.8 24.5
Table 5. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 3.2%. The maximum stress before unloading is 504.5 MPa Specimen 3.1 3.2 3.3
B (mm)
W (mm)
ac (mm)
PQ (N)
Kio (MPax/m)
12.70 12.69 12.72
25. I0 25.13 25.09
12.53 12.56 12.56
4343.8 4437.5 4187.5
23.3 23.8 22.5
Table 6. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 3.96%. The maximum stress before unloading is 520.2 MPa Specimen 4.1 4.2 4.3
B (mm)
W (mm)
ac (mm)
PQ (N)
KIQ (MPax/m)
12.65 12.66 12.67
24.94 24.93 24.95
12.63 12.67 12.75
3984.4 3890.6 3843.8
22.2 21.8 21.7
Table 7. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 5.1%. The maximum stress before unloading is 526.6 MPa Specimen 5.1 5.2 5.3
B (mm)
W (mm)
a¢ (mm)
PQ (N)
KIQ (MPax/m)
12.57 12.60 12.58
24.82 24.92 24.85
12.69 12.39 12.59
3937.5 4218.8 4062.5
22.6 22.9 22.9
being 1.06. It may be observed that the values of KIQ decrease as compared to values obtained for "virgin" material. Moreover, if a yield stress was measured for each of these specimens after the overload is induced, it would be greater than that of the unstrained material. The value of the stress just before unloading is given in each of Tables 3-7. Each of these values is close to the current yield stress for each plastic strain. Hence, the thickness and crack length requirement for a valid test would decrease. Nonetheless, the results are presented as KIQ in the tables. The KtQ values are plotted in Fig. 1 as open circles. The general decrease as a function of overstrain can be observed in the graph. It appears that at an overstrain of 5.1%, the value of KIQ begins to increase, although it is well below the value obtained for the unstrained material.
4. FRACTOGRAPHIC EXAMINATION The fracture surfaces at the boundary between fatigue crack propagation and unstable fracture were examined in a scanning electron microscope. In Figs 2(a)-(c) and Figs 2(d)-(f), fracture surfaces from specimens 004 and 4.1, respectively, are exhibited. Results for specimen 004 which was taken from as-received material are presented in Table 2; results for specimen 4.1 which was subjected to a 3.96% overstrain before specimen fabrication are presented in Table 6. It may be observed in Figs 2(b) and (e) that there is a distinct demarcation between the regions
70
L. BANKS-SILLS and I. D U N Y E KIQ
L 30/
(MPa ~r~)
o experiment • model [91
~¢
26 24 22 20
8 I 1.0
I 2.0
l 3.0
ep(%)
I 4.0
I 5.0
I 6.0
,
Fig. I. Fracture toughness vs induced permanent set determined experimentally and from a micromechanistic model.
of fatigue crack propagation and fast fracture. At the enlargement of Figs 2(c) and (f), the fatigue regions of both specimens are characterized by a rather smooth, elongated stalagmite type structure. In Figs 2(a) and (d), the fast fracture regions of both specimens appear to be full of voids which is characteristic of plastic deformation. There do not seem to be any apparent differences between the fracture surfaces of the two specimens which differ by the amount of overstrain to which each was subjected.
5. DISCUSSION AND C O N C L U S I O N S Fracture toughness was measured for specimens which were subjected to various levels of tensile overstrain. It was observed that there was a general degradation of the toughness values in comparison to as-received material. The maximum decrease was measured to be approximately 20%. A slight rise in the fracture toughness is observed at a level of about 5% overstrain. Testing conditions were maintained so as to reduce the residual stresses as much as possible. This was done in order to separate the effect of increased current yield stress from that of residual stresses. The current yield stress is then nearly a constant throughout the specimen width. Clearly, as overstrain increases, the current yield stress increases. It has been observed for many metals that as the yield stress is increased by heat treatment, fracture toughness decreases[16, 17]. In general, heat treatment changes the size of obstacles in the material which inhibit dislocation movement and hence may decrease dislocation density; whereas, mechanical treatment tends to increase dislocation density. A micro-mechanistic model was proposed in ref. [9] to determine Kic as a function of temperature for mild steel. The temperatures were sufficiently low so that unstable cleavage fracture of cracked specimens occurred. A critical tensile stress ar directly ahead of the crack tip for unstable cleavage fracture is determined from a model presented in ref. [18]. It was shown that 2O'y., o'f -~- - ~ - ( 1 q- ~r/2),
(1)
where a¥ is the yield stress. Knowledge of the critical tensile stress, together with an elastoplastic analysis of the tensile stress ahead of a crack tip in an elastic perfectly plastic material, allows prediction of Knc as the yield stress changes as a function of temperature. In employing this model, the critical cleavage fracture stress is obtained by substituting into eq. (1) the yield stress of the virgin material; it is found that af = 1342 MPa. This value may be used to determine an intensification factor which varies as the current yield stress ao changes for each tensile overload. This, together with an elasto-plastic finite element analysis presented in ref.[19], allows one to determine X/(K/ao) 2, where X is the distance ahead of the crack tip and K is the stress intensity factor. In that study, small scale yielding conditions were assumed with plane strain loading of an elastic-plastic power hardening material. The solution for strain
Effect of plastic strain on fracture toughness
71
--10 ~ m
Fig. 2. Photographs of fracture surfaces produced by a scanning electron microscope. (a) Region of fast fracture, (b) region of boundary between fatigue and fast fracture and (c) fatigue region from specimen 004. (d) Region of fast fracture, (e) region of boundary between fatigue and fast fracture and (f) fatigue region from specimen 4.1.
Effect of plastic strain on fracture
toughness
73
hardening parameter n = 0.1 is chosen for this analysis. In order to obtain KI, at each stress level, a characteristic distance X is required. Although it was postulated in ref. [9] that the critical tensile stress must be attained for a distance of two grains ahead of the crack tip, in ref.[20] other characteristic distances were determined. In order to obtain the grain size for the material studied here, a metallographic material sample was prepared and etched for 1 min with Keller’s etch. The cracks in the three-point bend specimens were taken to be parallel with the rolling direction. The average grain size in that direction was found to be about 500 pm, whereas it was found to be 30 ,um in the perpendicular direction. Employing this grain size or twice its value as X leads to unrealistic values of K,,. If a characteristic length X = 36 pm is chosen, then the values in Fig. 1 shown as filled squares are the calculated values. It may be observed that the trend of the experimental and calculated values are similar. From a practical point of view, it should be noted that in structures which are subjected to a tensile overload producing plastic strains, the fracture toughness may decrease. This has been shown both experimentally and from a micro-mechanistic model. The experimental results show a decrease of 6.6% at 1% prestrain, 11.8% at 2% prestrain, 13.6% at 3% prestrain, 19.5% at 4% prestrain and 16.1% at 5% prestrain. Acknol~,ledgeme/r?rs-We would like to thank Dr Nahum Travitsky for helpful discussions and Dr Yossi Lereah for his assistance with the scanning electron microscope. In addition. we are grateful to a reviewer for suggesting consideration of the micro-mechanistic model presented here.
REFERENCES 1. Smith. D. J. and Garwood, S. J.. The significance of prior overload on fracture resistance: a critical review. Int. J. Press. Vess. Piping, 1990, 41, 255-296. 2. Clayton, J. Q. and Knott, J. F., Observation of fibrous fracture modes in prestrained low alloy steel. Mercrl Sci., 1976, 10, 63-71. 3. Chipperfield, C. G., Detection and toughness characterisation of ductile crack initiation in 316 stainless steel. fnr. J. Fracture. 1976. 12, 873-886. 4. Willoughby, A. A., Pratt, P. L. and Turner, C. E., The meaning of elastic-plastic fracture criteria during slow crack growth. Int. J. Fracture, 1981, 17, 449-466. 5. Amouzouvi. K. F. and Bassim, M. N., Determination of fracture toughness from stretch zone width measurement in predeformed AISI type 4340 steel. Mafer-. Sci. Engng, 1982, 55, 63-71. 6. Amouzouvi, K. F. and Bassim, M. N., Effect of the type of prior straining on the fracture toughness of AISI 4340 steel. Mater. Sci. Engng, 1983, 60, 1-5. 7. Arora, I’. R., Raghavan, M. R. and Prasad, Y. V. R. K., Effect of prestrain on fracture toughness of rolled mild steel with significant inclusion content. J. Test. Ed., 1988, 16, 298-304. 8. Bar-On, I., Tuler, F. R. and Howerton, W. M., Effect of prestrain on the J-resistance curve on HY-100 steel. In Nonlinear Fracture Mechanics: Volume II-Elastic-Plastic Fracture, ASTM STP 995. ed. J. D. Landes, A. Saxena and J. G. Merkle. American Society for Testing and Materials, Philadelphia, 1989. pp. 244-258. 9. Ritchie. R. O., Knott, J. F. and Rice, J. R., On the relationship between critical tensile stress and fracture toughness in mild steel. J. Mech. Phys. So/i&, 1973, 21, 395-410. 10. ASM Handbook, Properties and Selection: Noqferrous Allo~~s and Special-Purpose Materials, Vol. 2. ASM International, U.S.A., 1993, p. 20. 11. Plane-strain fracture toughness of metallics materials. E 399-83. 1989 Annual Book of ASTM Standard~y,Vol. 03.01, American Society for Testing and Materials, Philadelphia, U.S.A., 1989, pp. 487-511. 12. Plane-strain fracture toughness testing of aluminum alloys. B 645-84. 1989 Annual Book qf ASTM Standards, Vol. 03.01, American Society for Testing and Materials, Philadelphia, U.S.A., 1989, pp. 75-77. 13. Broek. D., The Practical Use @Fracture Mechanics. Kluwer, Dordrecht, 1988, p. 211. 14. Banks-Sills, L. and Sherman, D.. J,, fracture testing of a plastically deforming material. Inr. J. Fracture, 1991. 50, 15-26. 15. Verification of specimen alignment under tensile loading, E 1012-89. 1989 Annual Book of ASTM Standards, Vol. 03.01. American Society for Testing and Materials, Philadelphia, U.S.A., 1989, pp. 770-777. 16. Jones, M. H. and Brown, W. F., Jr, The influence of crack length and thickness in plane strain fracture toughness tests. In Review of Developments in Plane Strcrin Frncture Toughness Testing, ASTM-STP 463, ed. W. F. Brown. American Society .for Test&g and Materials, Philadelphia. U.S.A., 1970. pp. 63-101. 17. Militarv handbook. Vol. I. U.S. Denartment of Defense. MIL-HDBK-SE. 1986. 18. Smith, i.. Cleavage fracture in mild’steel. ht. J. Fracture, 1968, 4, 131-145. 19. Tracey, D. M., Finite element solutions for crack-tip behavior in small-scale yielding. J. Engng Mater. Technoi., 1976,98, 146-151. 20. Curry, D. A. and Knott, J. F., The relationship between fracture toughness and microstructure in the cleavage fracture of mild steel. Metal Sci., 1976, 10, l-6. (Received 15 Nowmher 1995)
Engineering Fracture Mechanics Vol. 57, No. 1. pp. 67 73, 1997
PIh S0013-7944(96)00134-8
A NOTE
ON
THE
EFFECT
FRACTURE
OF
~. 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain oo13-7944/97 $17.oo + o.oo
PLASTIC
STRAIN
ON
TOUGHNESS
LESLIE BANKS-SILLS and I N N A D U N Y E The Dreszer Fracture Mechanics Laboratory, Department of Solid Mechanics, Materials and Structures, The Fleischman Faculty of Engineering, Tel Aviv University, 69978 R a m a t Aviv, Israel
Abstract--The fracture
toughness Ktc is employed regularly to predict catastrophic failure of many structures, In this study, experiments are carried out on three-point bend aluminum alloy (AI 7075T7351) specimens. The material from which the specimens are fabricated is subjected to several uniform tensile overloads. The overload causes a constant plastic strain within the material. It is seen that as the overstrain level is increased, the fracture toughness is reduced up to a factor of approximately 20%. A micro-mechanistic model is employed to determine KI~ values from the current yield stress. The trend shown by the model is similar to that determined by the tests. (~) 1997 Elsevier Science Ltd
1. I N T R O D U C T I O N THE FRACTURE toughness Klc is employed regularly to predict catastrophic failure. Well before failure, many structural materials undergo fatigue loads and various overloads such that critical regions are subject to plastic deformation. The effect of prestrain has been examined in the case of steels, in particular, in their application to pressure vessels which undergo proof testing. Several situations are of interest: (1) warm prestressing, (2) an overload applied to a cracked body and (3) an overload applied to an intact body. A review of these subjects is presented in ref. [1]. In this study, the last situation is investigated by testing an aluminum alloy, A1 7075T7351, to determine the effect of permanent deformation on fracture toughness. Some of the results relating to this topic only and reported in the literature for steels are reviewed here; this list is incomplete. In ref. [2], HY-80 low strength steel was subjected to four levels of compressive prestrain. The Klc values were seen to increase by about 12% for prestrains up to 17%, whereas these values began to decrease thereafter by as much as 25% at 56% residual strain. In ref. [3], Jic and critical crack opening displacement values were measured for 316 stainless steel. These values were seen to decrease as the percent of cold rolling increased from zero to 30%; the decrease was more than 60% at the highest prestrain. Mild steel, En32B, was compressed by nominal strains of 10% and 20% [4]. Initiation J values were determined and seen to decrease by as much as 75% depending upon crack orientation. AISI-4340 steel was investigated in refs [5, 6]. Material was prestrained by both cold rolling (compression) and tension. Fracture toughness tests were conducted on specimens machined from this material. The same trends were observed in both cases. The fracture toughness increased as much as 4.6 times its value at the annealed state as the prestrain level increased to 2%. It then decreased until at 10%, it reached a level approximately 25% less than that determined for the annealed material. The effect of two levels of prestrain on the stress intensity level of mild rolled steel was investigated in ref. [7]. Specimens were fabricated from prestrained long rectangular rods. It was found that at two values of the load line displacement, the stress intensity factor decreases for 3% prestrain and increases for 7% prestrain, as compared to virgin material. In ref. [8], HY-100 steel was subjected to prestrains of 5, 6, 8 and 10%. The measured values of Jlc decreased by about 25% at 10% prestrain as compared to material which was not subjected to a prestrain. In this investigation, long aluminum alloy, A1 7075-T7351, specimens are subjected to several tensile overloads creating different levels of plastic deformation with residual stresses minimized. First, the fracture toughness of this material is determined by testing four three-point bend specimens. The results are presented in Section 2. Then, in the form of long dog-bone specimens, the material is subjected to five different tensile overloads. Three-point bend specimens are fabricated from this material which contains permanent deformation or overstrain. Fracture toughness tests are carried out on these specimens. The results which are described in Section 3 67
L. BANKS-SILLS and I. D U N Y E
68
Table I. Chemical composition by percent of AI 7075-T7351 [10] Si
Fe
Cu
Mn
Mg
Cr
Zn
Ti
0.4
0.5
1.2 2.0
0.3
2.1-2.9
0.18-0.28
5.1-6.1
0.2
demonstrate a clear effect on the fracture toughness. In Section 4, a fractographic examination of crack surfaces is presented. A micro-mechanistic model[9] is employed in Section 5 to calculate the fracture toughness and compare with those values determined experimentally. 2. FRACTURE T O U G H N E S S TESTING The aluminum alloy, A1 7075-T7351, of nominal thickness 13 mm has been selected for study. A typical chemical composition is given in Table 1 [10]. Four fracture toughness tests in the T - L direction were carried out with an Instron loading machine (model 1341) on threepoint bend specimens according to ASTM standards[11,12]. Guides were added to the standard Instron three-point bend test fixture which position,s the specimen so that the load could be placed exactly at the span center and the span S is precisely 102 ram. All specimens were precracked from a chevron notch at 10 Hz with R = 0.1. The pre-cracking procedure fulfilled all restrictions imposed by the standard. Specimen measurements and results are presented in Table 2. All test records were of Type I. The largest ratio of Pmax/PQfor these tests was 1.04 which is well within the limitation for a valid Kic test. The 0.2% yield stress in the unstrained condition was found to be 452.2 MPa. According to this, the specimen thickness B and crack length at fracture ac should be at least 18.5 mm when the factor 5 (KiQ/aV) 2 is employed. The minimum factor of 3.5 instead of 5 is obtained with specimen number 002. Although these results coincide with similar results given in the literature for this material[13, 14], none of the results may be considered valid fracture toughness values according to this criterion in ref.[12]. The average value of K I Q is seen to be 27.2 MPax/-m. 3. FRACTURE TOUGHNESS TESTING OF OVERSTRAINED MATERIAL Long dog-bone specimens were fabricated with nominal overall length 630 mm and a gage length of 390 mm. These specimens were subjected to five different tensile overloads perpendicular to the material rolling direction producing a plastic permanent set or overstrain of 0.96, 2.0, 3.2, 3.96 and 5.1%. The tensile overload was induced in an Instron loading machine (model 1250). Before inducing the plastic deformation, the alignment of the load system and specimens were examined according to the ASTM standard E 1012-89115]. Three sets of four strain gages were placed on the specimens at the center of the gage area and equally spaced at 142 mm from the center. The minimum and maximum percent of bending at any of these three positions was 3.3% and 8%, respectively, at an applied load of 78.5 kN. The percent of bending decreases as applied load increases. The dog-bone specimens were subjected to a maximum load of approximately 175 kN. Hence, in the range that the overload is induced, the percent of bending is much less, so that only very small residual stresses are assumed present in the specimens. After the overstrain was induced in each of five dog-bone specimens, three-point bend fracture toughness specimens were fabricated from the gage region. For each dog-bone, three specimens were fabricated. Fracture toughness tests were carried out according to the ASTM standard [11]. The pre-cracks were induced as described in the previous section. In Tables 3-7 the results are presented. All test records were Type I with the maximum value of Pmax/PQ Table 2. Fracture toughness test results for AI 7075-T7351. The yield stress a v = 452.2MPa Specimen 002 003 004 005
B (mm)
W(mm)
a~(mm)
Po(N)
KIQ ( M P a ~ m )
12.94 12.91 12.90 12.95
25.40 25.39 25.40 25.42
13.02 12.98 12.60 12.87
5093.8 4971.9 5312.5 5125.0
27.5 26.8 27.3 27.1
Effect of plastic strain on fracture toughness
69
Table 3. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 0.96%. The maximum stress before unloading is 476.1 MPa Specimen 1.1 1.2 1.3
B (mm)
W (mm)
ac (mm)
PQ (N)
KIQ (MPax/m)
12.87 12.86 12.87
25.21 25.26 25.20
12.73 12.85 12.78
4781.3 4718.8 4656.3
25.6 25.5 25.1
Table 4. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 2.0%. The maximum stress before unloading is 491.1 MPa Specimen 2.1 2.2 2.3
B (mm)
W (mm)
ac (mm)
PQ (N)
KIQ (MPax/m)
12.76 12.78 12.79
25.21 25.25 25.26
12.55 12.68 12.74
4468.8 4468.8 4562.5
23.6 23.8 24.5
Table 5. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 3.2%. The maximum stress before unloading is 504.5 MPa Specimen 3.1 3.2 3.3
B (mm)
W (mm)
ac (mm)
PQ (N)
Kio (MPax/m)
12.70 12.69 12.72
25. I0 25.13 25.09
12.53 12.56 12.56
4343.8 4437.5 4187.5
23.3 23.8 22.5
Table 6. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 3.96%. The maximum stress before unloading is 520.2 MPa Specimen 4.1 4.2 4.3
B (mm)
W (mm)
ac (mm)
PQ (N)
KIQ (MPax/m)
12.65 12.66 12.67
24.94 24.93 24.95
12.63 12.67 12.75
3984.4 3890.6 3843.8
22.2 21.8 21.7
Table 7. Fracture toughness tests results for AI 7075-T7351 with a permanent set of 5.1%. The maximum stress before unloading is 526.6 MPa Specimen 5.1 5.2 5.3
B (mm)
W (mm)
a¢ (mm)
PQ (N)
KIQ (MPax/m)
12.57 12.60 12.58
24.82 24.92 24.85
12.69 12.39 12.59
3937.5 4218.8 4062.5
22.6 22.9 22.9
being 1.06. It may be observed that the values of KIQ decrease as compared to values obtained for "virgin" material. Moreover, if a yield stress was measured for each of these specimens after the overload is induced, it would be greater than that of the unstrained material. The value of the stress just before unloading is given in each of Tables 3-7. Each of these values is close to the current yield stress for each plastic strain. Hence, the thickness and crack length requirement for a valid test would decrease. Nonetheless, the results are presented as KIQ in the tables. The KtQ values are plotted in Fig. 1 as open circles. The general decrease as a function of overstrain can be observed in the graph. It appears that at an overstrain of 5.1%, the value of KIQ begins to increase, although it is well below the value obtained for the unstrained material.
4. FRACTOGRAPHIC EXAMINATION The fracture surfaces at the boundary between fatigue crack propagation and unstable fracture were examined in a scanning electron microscope. In Figs 2(a)-(c) and Figs 2(d)-(f), fracture surfaces from specimens 004 and 4.1, respectively, are exhibited. Results for specimen 004 which was taken from as-received material are presented in Table 2; results for specimen 4.1 which was subjected to a 3.96% overstrain before specimen fabrication are presented in Table 6. It may be observed in Figs 2(b) and (e) that there is a distinct demarcation between the regions
70
L. BANKS-SILLS and I. D U N Y E KIQ
L 30/
(MPa ~r~)
o experiment • model [91
~¢
26 24 22 20
8 I 1.0
I 2.0
l 3.0
ep(%)
I 4.0
I 5.0
I 6.0
,
Fig. I. Fracture toughness vs induced permanent set determined experimentally and from a micromechanistic model.
of fatigue crack propagation and fast fracture. At the enlargement of Figs 2(c) and (f), the fatigue regions of both specimens are characterized by a rather smooth, elongated stalagmite type structure. In Figs 2(a) and (d), the fast fracture regions of both specimens appear to be full of voids which is characteristic of plastic deformation. There do not seem to be any apparent differences between the fracture surfaces of the two specimens which differ by the amount of overstrain to which each was subjected.
5. DISCUSSION AND C O N C L U S I O N S Fracture toughness was measured for specimens which were subjected to various levels of tensile overstrain. It was observed that there was a general degradation of the toughness values in comparison to as-received material. The maximum decrease was measured to be approximately 20%. A slight rise in the fracture toughness is observed at a level of about 5% overstrain. Testing conditions were maintained so as to reduce the residual stresses as much as possible. This was done in order to separate the effect of increased current yield stress from that of residual stresses. The current yield stress is then nearly a constant throughout the specimen width. Clearly, as overstrain increases, the current yield stress increases. It has been observed for many metals that as the yield stress is increased by heat treatment, fracture toughness decreases[16, 17]. In general, heat treatment changes the size of obstacles in the material which inhibit dislocation movement and hence may decrease dislocation density; whereas, mechanical treatment tends to increase dislocation density. A micro-mechanistic model was proposed in ref. [9] to determine Kic as a function of temperature for mild steel. The temperatures were sufficiently low so that unstable cleavage fracture of cracked specimens occurred. A critical tensile stress ar directly ahead of the crack tip for unstable cleavage fracture is determined from a model presented in ref. [18]. It was shown that 2O'y., o'f -~- - ~ - ( 1 q- ~r/2),
(1)
where a¥ is the yield stress. Knowledge of the critical tensile stress, together with an elastoplastic analysis of the tensile stress ahead of a crack tip in an elastic perfectly plastic material, allows prediction of Knc as the yield stress changes as a function of temperature. In employing this model, the critical cleavage fracture stress is obtained by substituting into eq. (1) the yield stress of the virgin material; it is found that af = 1342 MPa. This value may be used to determine an intensification factor which varies as the current yield stress ao changes for each tensile overload. This, together with an elasto-plastic finite element analysis presented in ref.[19], allows one to determine X/(K/ao) 2, where X is the distance ahead of the crack tip and K is the stress intensity factor. In that study, small scale yielding conditions were assumed with plane strain loading of an elastic-plastic power hardening material. The solution for strain
Effect of plastic strain on fracture toughness
71
--10 ~ m
Fig. 2. Photographs of fracture surfaces produced by a scanning electron microscope. (a) Region of fast fracture, (b) region of boundary between fatigue and fast fracture and (c) fatigue region from specimen 004. (d) Region of fast fracture, (e) region of boundary between fatigue and fast fracture and (f) fatigue region from specimen 4.1.
Effect of plastic strain on fracture
toughness
73
hardening parameter n = 0.1 is chosen for this analysis. In order to obtain KI, at each stress level, a characteristic distance X is required. Although it was postulated in ref. [9] that the critical tensile stress must be attained for a distance of two grains ahead of the crack tip, in ref.[20] other characteristic distances were determined. In order to obtain the grain size for the material studied here, a metallographic material sample was prepared and etched for 1 min with Keller’s etch. The cracks in the three-point bend specimens were taken to be parallel with the rolling direction. The average grain size in that direction was found to be about 500 pm, whereas it was found to be 30 ,um in the perpendicular direction. Employing this grain size or twice its value as X leads to unrealistic values of K,,. If a characteristic length X = 36 pm is chosen, then the values in Fig. 1 shown as filled squares are the calculated values. It may be observed that the trend of the experimental and calculated values are similar. From a practical point of view, it should be noted that in structures which are subjected to a tensile overload producing plastic strains, the fracture toughness may decrease. This has been shown both experimentally and from a micro-mechanistic model. The experimental results show a decrease of 6.6% at 1% prestrain, 11.8% at 2% prestrain, 13.6% at 3% prestrain, 19.5% at 4% prestrain and 16.1% at 5% prestrain. Acknol~,ledgeme/r?rs-We would like to thank Dr Nahum Travitsky for helpful discussions and Dr Yossi Lereah for his assistance with the scanning electron microscope. In addition. we are grateful to a reviewer for suggesting consideration of the micro-mechanistic model presented here.
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