DEFINITION OF LOADING RATE AND EFFECTS ON …

Transactions, SMiRT-22

San Francisco, California, USA - August 18-23, 2013 Division II

DEFINITION OF LOADING RATE AND EFFECTS ON DETERMINATION OF DYNAMIC FRACTURE TOUGHNESS AND

TRANSITION TEMPERATURE T0,X ACCORDING TO ASTM E1921 AT ELEVATED LOADING RATES

Uwe Mayer1, Stefan Offermanns1

1 Materials Testing Institute (MPA) University of Stuttgart, Germany

ABSTRACT

ASTM E1921 (2013) describes the determination of the reference temperature T0,X for the

loading rate X in the transition range, where X is the order of magnitude of the average loading rate of the tests evaluated.

Because this rate is only defined for the linear-elastic part of a test, the aim of this analysis is to find a definition for the loading rate, valid for tests showing not only linear-elastic but also plastic behavior.

Tests at -20°C on specimens of 22 NiMoCr 3 7 steel (A 508 Cl.2), performed with different specimen geometry and loading devices in the range from dK/dt = 105 MPa√m s-1 to dK/dt = 3x106 MPa√m s-1, were evaluated and the progression of the stress near the crack tip calculated in numerical simulations was analyzed.

A proposal for an alternative definition of the loading rate in the transition range of fracture toughness is analyzed and examined.

INTRODUCTION

Commonly different parameters are used for characterizing the loading rate of linear-elastic and

elastic-plastic fracture mechanics test. For linear-elastic tests dK/dt can be kept approximately constant during the test, for elastic-plastic tests dJ/dt is constant after an initial acceleration during the linear-elastic part of the test. The loading rate dK/dt for J-integral initiation values, Eisele and Roos (1991), can only be used for the results of linear-elastic tests, otherwise dJ/dt has to be used as a characteristic parameter of the loading rate. For the use of a Master Curve evaluation according to ASTM E1921 in the transition range of fracture toughness, results from both types of tests are used: fracture toughness K for linear-elastic tests and formally calculated values KJ from J for elastic-plastic tests. The open question regards the relevant loading rate, especially if different test series are compared, e.g. one test series with unstable crack initiation during linear-elastic loading and the other one with similar KJ-values calculated formally from J-values, being elastic-plastic due to smaller dimensions. A unified parameter for the loading rate, valid for both, linear-elastic and elastic-plastic fracture mechanics tests would be preferable for the identification of the loading rate in a Master Curve evaluation.

LOADING RATE DEFINITION IN EXISTING STANDARDS

Dynamic fracture mechanics testing is specified in annexes of the standards ASTM E399 (2013)

and ASTM E1820 (2013), Annex 13, 14 and 17 and also in BS7448-3 (2005). In these standards fracture mechanics values J and K are determined basically the same way as for quasi-static tests.

Loading rate for rapid loading KIc determination is defined in ASTM E1820, Annex 13, as KQ/t. In ASTM E1820, Annex 14 (rapid-load J-integral fracture toughness testing), two different loading rate quantities are defined: (dJ/dt)I measured before JQ(t), and (dJ/dt)T measured after JQ(t), where JQ(t) is the

22nd Conference on Structural Mechanics in Reactor Technology


provisional, rate dependent J Integral at the onset of stable crack extension. (dJ/dt)I is defined by using a linear regression analysis between 0.5 JQ(t) and JQ(t), even if the increase is quadratic over time (Figure 1). The second loading rate is defined as the slope of the J versus time data beyond maximum force.

Additional estimations of dK/dt and dJ/dt are given in ASTM E1820, Annex 17, for pre-cracked Charpy-type specimen (SE(B) 10/10). But there is no method given, to convert dJ/dt into dK/dt.

In BS 7448-3 two definitions for the loading rate are given: dKI/dt during the initial elastic loading of the specimen and the rate of change of the plastic component of the J integral dJp/dt, determined using the time interval for plastic deformation of the test specimen.

These different definitions for the different parts of a fracture mechanics test at elevated loading rate are both useful for characterizing the loading rates of the tests. Only if results from both, linear-elastic tests and elastic-plastic tests are assessed together to describe the influence of the loading rate on cleavage fracture toughness for a material a unified definition of the loading rate for both types of tests is needed. This applies especially to the Master Curve evaluation according to ASTM E1921.

Figure 1. Loading rate definition in ASTM E1820

PROPOSED DEFINITION OF LOADING RATE

Since the J-integral correlates quadratic with K, the question arises during application of ASTM

E1921 at high loading rates, if for the elastic-plastic range a quadratic increase of the J-integral leads to a loading rate comparable to linear-elastic tests.

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5

J [Nmm

‐1] resp. K

J[M

Pam

0.5]

Time t [ms]

KJJ0.5 ∙ JQJQ(dJ/dt)I (ASTM E1820)

tQ

ASTM E1820 (linear fit)(dJ/dt)I = 2.8 x 10

5 N mm‐1 s‐1

dK/dt = 5.1 x 105 MPam0.5 s‐1



However, usual testing conditions with constant displacement rate result in a linear increase of the J-integral over time in the plastic regime after the initial acceleration during the linear-elastic part of the test.

We analyze the correlation of the change over time of K and the change over time of J in the case of a linear-elastic fracture mechanics test for constant dK/dt:

(1)

/

(2)

(3)

solving for dK/dt leads to:

(4)

K = stress intensity factor (time series) E = Youngs modulus J = J-Integral (time series) ν = Poisson’s ratio dK/dt = loading rate This means that the loading rate dK/dt in the elastic range, if it is transferred to J, is proportional

to the square root of the second derivative of J. In other words: a constant loading rate dK/dt in a linear-elastic fracture mechanics test means an accelerated course of J. The calculation of K from J for elastic-plastic tests is only formally. The intrinsic fracture mechanics parameter is the J-integral. The calculation is only performed to allow a comparison between the results of linear-elastic tests and elastic-plastic tests.

DISCUSSION OF RESULTS OBTAINED FROM TESTS AT HIGH LOADING RATE

Results of a research project investigating the correlation of dynamic crack initiation and crack

arrest, Böhme et al. (2012), that was funded by the German government, show differences of up to 30 K in T0,X obtained from linear-elastic test series and T0,X obtained from elastic-plastic test series with comparable dK/dt.

Tests at -20°C on specimens of 22 NiMoCr 3 7 steel (A 508 Cl.2) were performed with different specimen geometry and loading devices in the range from 105 MPa√m s-1 to 3x106 MPa√m s-1, Böhme et al. (2012). Two of the testing devices at IWM and MPA were special high rate servo-hydraulic machines (Instron VHS 100/20). These machines incorporate large hydraulic accumulators (2x 280 l), high flow rate servovalves (6400 l/min) and a special slack adapter such that almost constant displacement rates over the duration of the test can be achieved. The machines have a maximum load of 100 kN and a maximum loading rate of 20 m/s. More details are given in Roos and Mayer (2003).

Force was measured using strain gauges directly on the specimen, Klenk et.al (1994) and Hojo et al. (2008). An example for the instrumentation of a compact tension specimen (C(T)) is given in Figure 2. Crack opening displacement (COD) was measured with an optical device. Details are described in Mayer (2012).



Tests with compact tension specimens with thickness of 1 inch 1T C(T) (Figure 4 and Figure 6) show nearly pure linear-elastic behavior.

Figure 2. Force measurement and crack tip strain gauge application on a C(T) specimen

Figure 3. Master Curve 1T C(T) tests (2x105 MPa√m s-1)

Figure 4.Force vs. COD curve 1T C(T) tests

(2x105 MPa√m s-1)

Figure 5. Master Curve 1T C(T) tests

(1x106 MPa√m s-1)

Figure 6. Force vs. COD curve 1T C(T) tests

(1x106 MPa√m s-1)

0

50

100

150

200

-80 -60 -40 -20 0 20 40 60 80

Fra

ctu

re T

ou

gh

ne

ss K

Id[M

Pa

m]

Temperature T [°C]

KJc,d_50%

1T(C)T dK/dt = 2 x 105 MPa√m s-1

KJc,d_5%

KIR

KJc_50% KJc_5%

T0,5 = +15 °C

0.0 0.2 0.4 0.6 0.8 1.00

5

10

15

20

25

30

35

40

Fo

rce

[kN

]

COD [mm]

CM07 CM08 CM09 CM10 CM11 CM12 CM13 CM14

0

50

100

150

200

-80 -60 -40 -20 0 20 40 60 80

Fra

ctu

re T

ou

gh

ne

ss K

Id[M

Pam

]

Temperature T [°C]

KJc,d_50%

1T C(T) dK/dt = 1 x 106 MPa√m s-1

KJc,d_5%

KIR

KJc_50% KJc_5%

T0,6 = +17 °C

0.0 0.2 0.4 0.6 0.8 1.00

5

10

15

20

25

30

35

40

Fo

rce

[kN

]

COD [mm]

CM_15 CM_17 CM_18 CM_19 CM_20 CM_21 CM_22 CM_23 CM_24 CM_25



The below given results of several series of tests with single edge bend specimens SE(B) 40/20 and SE(B) 10/10 (pre-cracked Charpy, PCC) specimens were performed at Fraunhofer IWM and special high rate measuring techniques were applied, details of which are described in Böhme and Reichert (2012). For example, near crack tip strain gauges were used to measure the local loading behavior and to detect crack initiation, according to Böhme and Kalthoff (1983). In addition, high speed video cameras in combination with digital image correlation (DIC) analysis were applied to determine the crack mouth opening curve CMOD(t) for an impacted SE(B)-specimen, see Böhme and Reichert (2012).

Results of SE(B) 40/20 are given in Figure 8 showing nearly pure linear-elastic behavior. Also small SE(B) 10/10 (pre-cracked Charpy, PCC) specimens, loaded in the servo-hydraulic high rate machine with a displacement rate of about 6 m/s (Figure 10) resulting in a loading rate of 3x106 MPa√m s-1, which all show nearly pure linear-elastic behavior.

Figure 7. Master Curve SE(B) 40/20 tests (5x105 MPa√m s-1)

Figure 8. Force vs. CMOD curve SE(B) 40/20 tests

(5x105 MPa√m s-1)

Figure 9. Master Curve SE(B) 10/10 tests (3x106 MPa√m s-1)

Figure 10. Force vs. CMOD curve SE(B) 10/10

tests(3x106 MPa√m s-1)

The tests of the series with a loading rate of up to 3x105 MPa√m s-1 (Figure 4, Figure 8, Figure 12 and Figure 14) meet the minimum test time (tw) requirement of Annex A14 of ASTM E1820 on rapid load J-integral testing:

t > tw (5)

tw =

(6)

ks = specimen load-line stiffness,

Meff = effective mass of the specimen, taken here to be half of the specimen.

0

50

100

150

200

-80 -60 -40 -20 0 20 40 60 80

Fra

ctu

re T

ou

gh

ne

ss K

Id[M

Pam

]

Temperature T [°C]

KJc,d_50%

SEB 40/20 (IWM)dK/dt = 5 x 105 MPa√m s-1

KJc,d_5%

KIRKJc_50% KJc,d_5%

T0,5 = +14 °C

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500

5

10

15

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25

30

35

40

45

50

55

60

Fo

rce

[kN

]

CMOD [mm]

TN1-SEB40-05 TN1-SEB40-07 TN1-SEB40-09 TN1-SEB40-11 TN1-SEB40-15 TN1-SEB40-17 TN1-SEB40-19 TN1-SEB40-03

0

50

100

150

200

-80 -60 -40 -20 0 20 40 60 80

Fra

ctu

re T

ou

gh

nes

s K

Id[M

Pa

m]

Temperature T [°C]

KJc,d_50%


KJc,d_5%

KIR

KJc_50% KJc,d_5%

T0,6 = +23 °C

0.0 0.1 0.2 0.30

2

4

6

8

10

For

ce [k

N]

CMOD [mm]

TN1-SEB10-08 TN1-SEB10-13 TN1-SEB10-18 TN1-SEB10-28 TN1-SEB10-28 TN1-SEB10-33 TN1-SEB10-38 TN1-SEB10-43 TN1-SEB10-48 TN1-SEB10-53 TN1-SEB10-03



Fracture toughness values for instability were converted into 1T values. Evaluation according to ASTM E1921 resulted in T0,5 (Figure 3 and Figure 7) and T0,6, respectively (Figure 5 and Figure 9) of 15°C resp. 17°C for 1T C(T) tests, 14°C for SE(B) 40/20 and 23°C for SE(B) 10/10 tests, see Böhme and Reichert (2012).

Quite different results were obtained testing SE(B) 10/10 (PCC) specimens at about 2x105 MPa√m s-1. Tests using a displacement rate of about 1 m/s were performed using both, the pendulum impact testing machine and the servo-hydraulic testing machine. Evaluation according to ASTM E1921 resulted in T0,5 of -7°C (Figure 11) and -16°C (Figure 13) which is a significant shift of 20-30K, when compared to the before mentioned test series and is much more than the difference, that can be expected for various test series in general. However, these results and reference temperatures agree well with the rate dependent behavior as can be estimated by an empirical equation given in ASTM E1921. This behavior is discussed in detail by Böhme et al. (2013).

Figure 11. Master Curve SE(B) 10/10 tests (3x105 MPa√m s-1), pendulum 1m/s

Figure 12. Force vs. displacement curve SE(B) 10/10 tests (3x105 MPa√m s-1), pendulum 1m/s

Figure 13. Master Curve SE(B) 10/10 tests (2x105 MPa√m s-1), servo-hydraulic 0.6 m/s

Figure 14. Force vs. CMOD curve SE(B) 10/10 tests(2x105 MPa√m s-1), servo-hydraulic 0.6 m/s

Since the SE(B) 10/10 (PCC) test series with a loading rate of 3x106 MPa√m s-1 (Figure 9) yields

similar results as the tests with the larger 1T C(T) and the SE(B) 40/20 specimens, specimen size and type of geometry seem not be the origin of this discrepancy.

Looking for other differences in these tests, it is obvious, that in both SE(B) 10/10 (PCC) test series at 2(3)x105 MPa√m s-1 a large number of tests behave elastic-plastic, while in contrast all the other tests have no or only little deviation from pure linear elastic behavior.

0

50

100

150

200

-80 -60 -40 -20 0 20 40 60 80

Fra

ctu

re T

ou

gh

ne

ss K

Id[M

Pam

]

Temperature T [°C]

KJc,d_50%


KJc,d_5%

KIRKJc_50% KJc,d_5%

T0,5 = -7 °C0.0 0.2 0.4 0.6 0.8 1.0

0

5

10

For

ce [k

N]

Displacement [mm]

TN1-SEB10-02 TN1-SEB10-07 TN1-SEB10-09 TN1-SEB10-12 TN1-SEB10-14 TN1-SEB10-17 TN1-SEB10-19 TN1-SEB10-21 TN1-SEB10-22 TN1-SEB10-24 TN1-SEB10-26 TN1-SEB10-29 TN1-SEB10-31 TN1-SEB10-32 TN1-SEB10-34 TN1-SEB10-36 TN1-SEB10-37 TN1-SEB10-39 TN1-SEB10-41 TN1-SEB10-42 TN1-SEB10-44 TN1-SEB10-46 TN1-SEB10-47 TN1-SEB10-51 TN1-SEB10-54 TN1-SEB10-55 TN1-SEB10-69 TN1-SEB10-79 TN1-SEB10-86 TN1-SEB10-90 TN1-SEB10-96 TN1-SEB10-100

0

50

100

150

200

-80 -60 -40 -20 0 20 40 60 80

Fra

ctu

re T

ou

gh

ne

ss K

Id[M

Pam

]

Temperature T [°C]

KJc,d_50%


KJc,d_5%

KIRKJc_50% KJc,d_5%

T0,5 = -16 °C

0.0 0.1 0.2 0.30

2

4

6

8

10

Fo

rce

[kN

]

CMOD [mm]

TN1-SEB10-05 TN1-SEB10-10 TN1-SEB10-15 TN1-SEB10-20 TN1-SEB10-20 TN1-SEB10-25 TN1-SEB10-30 TN1-SEB40-35 TN1-SEB10-40 TN1-SEB10-45 TN1-SEB10-50



Figure 15. Force-displacement curve of a pendulum test with a SE(B) 10/10 specimen at 1m/s, resulting in dK/dt =3x105 MPa√m s-1

Figure 16. First derivative of J(t) and KJ(t) Figure 15 shows the force-displacement curve for one of the tests with 1 m/s using the pendulum

machine. The data are fitted to a linear function in the beginning and to an exponential saturation curve for the plastic part of the test, so it is easier to derivate the data and to determine the loading rate. KJcd at start of unstable crack is 132 MPa√m , with the correction to a specimen thickness of 1 inch KJcd (1T) = 109 MPa√m. This value is lower than the limit for this specimen KJclimit = 180 MPa√m (KJclimit(1T) = 147 MPa√m), i.e. this is a valid toughness value according to ASTM E 1921. The first derivative of KJ and J is shown in Figure 16.

0

1

2

3

4

5

6

7

8

9

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Force [kN

)

Displacement [mm]

TN1‐SEB10‐12

Fit for SE(B) 10/10 result

1.E+03

1.E+04

1.E+05

1.E+06

0 0.1 0.2 0.3 0.4 0.5

dJ/dt [Nmm

‐1 s

‐1] resp. d

KJ/dt [M

Pam

0.5 s

‐1]

Time t [ms]

dKJ/dt

dJ/dt

(dJ/dt)I (ASTM E1820)

dK/dt (ASTM E1820)



Figure 17. Results for different definitions of loading rate The result of the calculation of dK/dt according to the proposed definition using d2J/dt2 is shown

in Figure 17. Above J=58 N/mm (KIJ = 116 MPa√m, KIJ(1T) = 96 MPa√m) dK/dt calculated with this definition declines below 105 MPa√m s-1, while the rate of KIJ calculated after conversion from J is near to 3x105 MPa√m s-1 for the entire test.

The loading rate at the time of unstable crack initiation, calculated with the proposed definition, was too low for this particular test, with given specimen geometry, displacement rate and temperature. Following this proposal the result should not be included in the determination of T0,5, as it has to be done according to the current edition of ASTM E1921.

This is the case for 6 out of 32 tests of this series with 1 m/s displacement rate using the pendulum machine and has a strong influence to the determined value for the reference temperature T0,5. This can be seen in Figure 11 as a population of data above 100 MPa√m. If we censored the KJcd(1T)-values higher than 96 MPa√m, as it would be done if the values were higher than KJclimit, T0,5 would be evaluated to 2°C instead of -7°C, calculated according to ASTM E1921.

In future work it will be investigated, if there are comparable results for tests with larger specimens like 1T C(T) and SE(B) 40/20, at a test temperature, when these specimens show elastic-plastic behavior.

ANALYSIS OF LOCAL STRESS HISTORY

The most important parameter for unstable crack initiation is the major principal stress, which

practically is the stress normal to the crack plane. The initial point for unstable crack propagation is situated very near to the tip of the fatigue pre-crack. Numerical and experimental investigations on the crack initiation point for specimens of different size and constraint showed larger distance to the crack tip for higher loads, Roos et al. (2006). This can be understood by the shift of the maximum of the major principal stress from the crack tip further into the ligament.

For linear elastic tests the major principal stress in the region, where the unstable crack starts, shows a sharp increase with crack opening displacement (COD). If plastic deformation starts to be a significant part of the macroscopic specimen behavior, the incline of the major principal stress with COD becomes more and more gentle, especially if the maximum moves towards the ligament with increasing

1.E+04

1.E+05

1.E+06

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

dK/dt [M

Pam

1/2s‐1]

Displacement [mm]

J [N

mm‐1]

J

dKJ/dt

dK/dt calculated using d2J/dt^2



distance from the fatigue pre-crack. Figure 18 shows the results of an analysis of the quasi-static loading of a 1T C(T) specimen.

Figure 18. Major principal stress vs. COD in the range 0.01 to .28 mm distance from the crack tip

The time history of this major principal stress does not play any role for the behavior of the

material as long as the test is quasi-static and there is no or only little sensitivity to the loading rate. This changes significantly for higher loading rates. Dynamic fracture tests are generally

performed using a constant displacement rate, thus the COD is proportional to time. In case of dynamic tests we can transfer these observations of the increase of the stress normal to the fracture plane with COD to the stress rate relating to time. This view on the local stress rate near the unstable crack initiation supports the conception that the loading rate is decreasing, if the test ceases to be globally linear-elastic.

CONCLUSIONS

A new definition of the loading rate is proposed for the transition range of fracture toughness.

This can be helpful for clarifying, why for different types of test series, evaluated according to the current version of ASTM E1921, differences of up to 30K for T0,X were determined (X is defined as the order of magnitude of dK/dt). Different loading rates may be one factor.

With the proposed definition the loading rate of each test can be checked to be within the scope. If not, censoring may be an option to determine a more accurate reference temperature. Further experimental and numerical investigations are needed for validation of this procedure.

The influence of other parameters, as adiabatic heating in the plastic zone, constraint and small amounts of ductile crack growth will be considered in future projects.

0.0 0.2 0.4 0.60

500

1000

1500

2000

No

rmal

str

ess

[MP

a]

COD [mm]

0.01mm 0.02mm 0.03mm 0.04mm 0.06mm 0.08mm 0.12mm 0.16mm 0.21mm 0.28mm

0

20

40

60

Force

Fo

rce

[kN

]



ACKNOWLEDGMENT The research project “Verification and further development of assessment

methods for dynamic crack initiation and crack arrest” was funded by the German Federal Ministry of Economy and Technology (BMWi, Project No. 1501368) on basis of a decision by the German Bundestag.

REFERENCES

ASTM E1921-13 (2013). “Standard Test Method for Determination of Reference Temperature, T0, for

Ferritic Steels in the Transition Range,” ASTM International, American Society for Testing and Materials, West Conshohocken, PA, USA.

ASTM E1820-11e (2013). “Standard Test Method for Measurement of Fracture Toughness,” ASTM International, American Society for Testing and Materials, West Conshohocken, PA, USA.

ASTM E399-12 (2012). “Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials,” ASTM International, American Society for Testing and Materials, West Conshohocken, PA, USA.

Böhme, W. and Kalthoff, J.F. (1983). Der Einfluß der Probengröße auf dynamische Effekte bei der KId Bestimmung im Kerbschlagbiegetest, Fraunhofer IWM Bericht W 3/83, Freiburg.

Böhme, W., Mayer, U., Reichert, T, Offermanns, S., Allmendinger, A., Hug, M., Schüler, J. and Siegele, D. (2012). “Überprüfung und Weiterentwicklung von Bewertungsmethoden für dynamische Rissinitiierung und Rissarrest, (Verification and further development of assessment methods for dynamic crack initiation and crack arrest),” BMWi-Vorhaben Nr. 150 1368.

Böhme, W., Reichert, T. (2012). Bestimmung und Bewertung bruchmechanischer Kennwerte bei hohen Rissbelastungsraten für den RDB-Stahl 22 NiMoCr 3 7, DVM-Tagung „Bruchvorgänge“, Darmstadt, Tagungsband, S. 245-254.

Böhme, W., Reichert, T. and Mayer, U. (2013). „Assessment of dynamic fracture toughness values KJc and reference temperatures T0,x determined for a German RPV steel at elevated loading rates according to ASTM E1921“, to be published at 22nd Int. Conf. on Structural Mechanics in Reactor Technology, SMiRT-22, San Francisco, USA.

BS 7448-3:2005 (2005). Fracture Mechanics Toughness Tests, Part. Method for Determination of Fracture Toughness of Metallic Materials at Rates of Increase in Stress Intensity Factor Greater than 3.0 MPa·m0.5s-1, BSI.

Eisele, U. and Roos, E. (1991). “Evaluation of different fracture mechanical J-integral initiation values with regard to their usability in the safety assessment of components,” Nucl Engng Des 1991; 130:237-247.

Hojo, K., Yoshimoto, K., Yamamoto, R. Matsuoka, T. and Mayer, U. (2008). Application of Master Curve Method to Fracture Toughness Estimation of the Transport and Storage Cask Material, Proceedings of PVP2008, 2008 ASME Pressure Vessels and Piping Division Conference, PVP2008-61181, Chicago, Illinois, USA, July 27-31 2008.

Klenk, A., Link, T., Mayer, U. and Schüle, M. (1994). “Criteria for Crack Initiation in Elastic Plastic Materials Under Different Loading Rates”, Proceedings of the 10th Biennial European Conference on Fracture, ECF10, Berlin, Germany, 20-23 September 1994, pp. 431-436

Mayer, U. (2012). “Determination of Dynamic Fracture Toughness at High Loading Rates,” Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition, IMECE2012-85383, Houston, Texas, USA, November 9-15 2012.

Roos, E., Eisele, U., Lammert, R., Restemeyer, D., Schuler, X., Seebich, H.-P., Seidenfuß, M., Silcher, H. and Stumpfrock, L. (2006). „Kritische Überprüfung des Masterkurven-Ansatzes im Hinblick auf die Anwendung bei deutschen Kernkraftwerken“, Forschungsvorhaben BMWi-FKZ 1501240, Abschlussbericht MPA Stuttgart.

Roos, E. and Mayer U. (2003), “Progress in testing sheet material at high strain rates”, J. Phys. IV 110, pp. 495-500.

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