Title:

Determination J1C of high strength steel material through unloading compliance test on a 3-point

bend specimen.

Objectives:

(a) Determine the value of J1C of the high strength steel material based on standard E813.

Introduction:

The accurate prediction of ductile fracture behavior plays an important role in structural

integrity assessments of critical engineering structures under fully plastic regime, including

nuclear reactors and piping systems. Many structural steels and aluminum alloys generally

exhibit significant increases in fracture toughness, characterized by the J-integral over the first

few mm of stable crack extension (Da), often accompanied by large increases in background

plastic deformation. Conventional testing programs to measure crack growth resistance (J–Da)

curves (also termed R-curves) routinely employ three-point bend, SE(B), or compact, C(T),

specimens containing deep, through cracks (a/W ≥ 0.5). [1]

This test method covers the determination of JIc , which can be used as an engineering

estimate of fracture toughness near the initiation of slow stable crack growth for metallic

materials. It applies specifically to geometries that contain notches and flaws and that are

sharpened with fatigue cracks. The recommended specimens are generally bend type that contain

deep initial cracks. The loading rate is slow and environmentally assisted cracking is assumed to

be negligible.

The recommended three-point bend specimen is a single edge-cracked beam having an

initial normalized crack length, ao/W, of 0.5 to 0.75. Overall span-to-width ratio, S/W is set at 4.

Specimen dimension requirements are based upon the ratio of J-integral to material effective

yield strength. Therefore, in specimen design, it is helpful to have a general idea of the expected

results in advance. Specimen configurations other than those recommended in this test method

may involve different validity requirements than those presently specified in this method.

For a deeply cracked bar in bending as shown in Fig (i). It was shown (Rice 1973), that

J= 2Bb∫0

θC

M dθC

Where:

B is the thickness of the bar

B = length of uncracked ligament ahead of crack

M = bending moment

θC is the bending angle due to introduction of crack

J=∫0

P

( ∂∆∂a )P

dP=∫0

M '

( ∂θ∂a )M '

dM '=∫0

M'

( ∂θ∂b )M 'dM '

M’ =M/b is the bending moment per unit thickness. Note that d∆ = dθ.ds and that dM=dP.ds.

Also b = (W-a), it follows that ∂∂a

=−∂∂b

Assume thatθ=f (M ' /b2), then

∂θ/∂b=∂ f (M ' /b2 )/∂b=2M ' /b3 f ' (M ' /b2 )=2M ' /b3 (b2∂θ/∂M ' )Hence,

Figure 1.0

Standard Test Method for J1C

The original standard procedure is described in ASTM E813 using either bend type or edge

notched specimen configurations. The load-line displacement must be measured (not the crack

mouth displacements as in case of K1C and CTOD testing). The currently adopted procedure is

described in ASTM E 1890-1999.

J is determined from the load vs load-line displacement from the following expressions:

J= ABbf ( aw )

Where;

A= area under the load vs load-line displacement

B= specimen thickness

B= initial uncracked ligament (W-a)

W= specimen width

Ao= initial crack length (including pre-cracking)

f ( aw ) = 2.0 for 3-pt bend specimen

=2.2 for compact tension specimen

To determine J initiation or the J value at the onset of crack growth, several identical specimens

are tested at different values of crack growth, ∆a. these specimens are then unloaded, heat tinted

to mark the crack growth broken open at low temperature. The values of J are then plotted

against ∆a as shown in Figure (1). Blunting lines are then drawn at crack extension (∆a) values

of 0.15 and 0.15mm. These lines have a slope of 2σflow. The intersection between the R-curve

regression line and the 0.15mm offset line defined JQ as shown. JQ = J1c as long as the following

size requirements are satisfied:

B ,b≥25 JQ /J ys

(Power law regression line: ¿ J=¿C1+C2∈(∆a)¿

Note: y=a+bx ,a= y−b x ,b=SxySxx

,

Sxy=1n∑ xy−x y ,

Sxx=1n∑ x2−x2

Figure 2.0:

Apparatus/Equipment:

1. Testing Machine:

a) Instron tensile/compress 100kN

2. Crack Opening Displacement Gauge

3. Single Notch Edge Bend (SNEB) specimen machine

4. Placom Digital Planimeter

5. Materials:

a) High strength steel material

B

BB

W

Methodology:

B = 25.0 mm, W= 50.0 mm, ao = 26.1 mm

Figure 3.0: 3-point bend specimen dimensions

Figure 4.0: 3-point bend specimen configuration

Bend specimen with plastic hinge.

Figure 5.0

∅= CPL

Fdy Bb2= δL

P=Fdy Bb

2

C L2 δ

∂P∂b

=2 FdyBb

C L2 =2Pb

∂P∂b

=−2 Pb

J=−1B ∫ ∂ P

∂a∂ S

¿ 2Bb∫PdS

¿ 2 ABb

∴ J R=2 ABb

Where; A= Area of plotted graph

B= Thickness of specimen

Blunting line; JQ=2 τ y∆a

Where; τ y= Yield Strength

∆ a= Crack extension

Therefore;

J1c=JQ; if B ,b≥25JQτ ys

Figure 6.0

Figure 7.0

Procedures:

1. Prepared the specimens according the standard configuration of Single Edge Notch Bend

(SENB) specimen. The material of the specimen is prepared from high strength steel

based on standard E813.

2. Prepared specimens are applied fatigue pre-cracking of 2mm using fatigue pre-cracking

machine.

3. Placed the clip gauge at the notch for measuring crack opening displacement.

4. Placed the specimen on the Single Edge Notch Bend (SENB) machine and applied load

on the specimen.

5. All data are recorded tabulated into a table.

6. Plotted graph of load versus plastic displacement, and find area under the curve for every

load.

7. Plotted graph of load versus crack extension, and find the value of JQ.

8. Analyst the data obtained from result and the graph.

9. Determined the value of JQ .

10. Checked the validity for J1c.

Result:

Data of specimen:

Elastic Modulud,E = 210 GPa

Poisson’s ratio,ν = 0.3

Yield strength = 600 MPa

Ultimate tensile strength = 710 MPa.

No.Load,P (kN)

Plastic Displacement,

δ (mm)

Crack Extension, ∆a

(mm)

Area under curve load vs plastic displacement, A

(kNmm)

J, (Nmm2/mm)

1 20.8 0 0.013 0 02 31.2 0.0032 0.020 0.016 0.0543 35.4 0.0110 0.023 0.069 0.2314 37.4 0.0200 0.025 0.136 0.4555 41.6 0.0560 0.031 0.429 1.4366 43.7 0.0920 0.036 0.733 2.4547 45.7 0.1460 0.044 0.770 2.5778 47.6 0.2280 0.055 1.730 5.7919 49.9 0.3490 0.071 2.930 9.80910 51.6 0.5250 0.091 4.300 14.39311 53.5 0.7770 0.128 7.600 25.43912 55.3 1.1300 0.183 11.130 37.25513 56.6 1.6300 0.321 16.870 56.46914 56.7 2.3200 0.723 24.800 83.01315 56.5 2.6600 0.928 29.170 97.64016 55.8 3.2500 1.290 35.570 119.06317 54.7 3.9600 1.740 43.770 146.51018 53.7 4.5100 2.080 49.400 165.35619 52.5 5.1300 2.480 55.600 186.10920 50.1 6.2000 3.170 66.700 223.26421 44.1 8.4300 4.670 88.200 295.23022 40.0 10.0900 5.810 103.100 345.10523 36.6 11.3700 6.700 112.230 375.66524 30.9 13.5400 8.230 127.200 425.77425 26.8 15.1900 9.410 137.640 460.720

Table 1.0

Sample of Calculations:

For example data number 14 at load,P = 56.7 kN

a) Calculate area under curve from graph of load versus plastic displacement.

By using Placom digital planimeter, at load 56.7 kN;

Area (A) = 24.800 kNmm

b) Calculate value of J;

f ( aw ) = 2.0 for 3-pt bend specimen

J= ABbf ( aw )

¿(24.800 )

(25 ) (50−26.1 )(2 )

¿83.013Nmm /mm2

c) Calculate value of J blunting;

J blunting = ( τUTS+τ ys )∆a

= (710+600 ) (0.723 )

= 947.13Nmm /mm2

d) From graph of J vs ∆a

JQ = 42.0 Nmm/mm2

e) Check the validity of JQ = J1c

B ,b≥25 JQ /τ ys

¿2542. 0600

¿1.75mm

B= 25.0 mm > 1.75mm

B= 23.9 mm > 1.75mm

Therefore, J1c = JQ = 42.0 Nmm/mm2

Discussion:

From the experiment, we are obtained the value of JQ by using unloading compliance technique

using 3-point bend specimen. The value of JQ is determined as value of J1c because it is satisfy

the validity rule.

The value is almost same compared with other students. The difference occurs because

the calculations involve value with four points. Besides that, the difference also occurs because

the range of data is too big until it is difficult to plot on the graph and find data that need.

Conclusion:

The value of the JQ obtained from this experiment is 42.0 Nmm/mm2. From the testing of the

validity of JQ, it was determine that this value satisfy the condition to be J1c. Therefore, the value

of JQ is also the value of J1c.

References:

1. Sebastian Cravero, Claudio Ruggieri, Estimation procedure of J-resistance curves for

SE(T) fracture specimens using unloading compliance, 23 January 2007, Engineering

Fracture Mechanics 74 (2007) 2735–2757.

2. Fracture Mechanics Fundamental and Applications, T.L Anderson, 2005, 3rd Edition,

Taylor and Francis Group.

3. Standard Test Method for J1C, A measure of fracture toughness, Standard E813-81.

4. Lab sheet of experiment J1c , determine the J1c of high strength steel material.