Determination of the residual crack extension resistance curves (
To describe the crack propagation in concrete structures, the crack extension resistance in terms of
The main requirement for determining crack extension resistance curve based on cohesive force distribution during crack propagation is to know the loadcrack mouth opening displacement (
The influence of temperature on the fracture properties was considered by several researchers, mainly on the fracture energy and material brittleness [
The main objective of this research is to determine the residual crack extension resistance (
According to
In order to develop the
Four stages of crack propagation during the fracture process.
Initial notch length
Critical notch extension
Fully developed crack zone
Formation of new stressfree crack length
The softening tractionseparation law is a priori to determine the
The bilinear softening tractionseparation law.
As a consequence, a general form of the simplified bilinear expression of the softening tractionseparation law is given as follows:
Different values of the break point (
The standard Green function [
There is no advancement in the initial notch length at this stage of loading and the body remains in elastic condition, subjected to small load (up to
The stable slow crack growth will take place until the effective crack extension
(a) For specimens subjected to temperatures less than 120°C, the critical CTOD_{
c} corresponding to maximum load
Two different situations for CTOD_{
c} and
When CTOD_{
c}
When CTOD_{
c}
The cohesive distribution of crack propagation stage II.
The linear distribution of cohesive force
The bilinear distribution of cohesive force
(b) For specimens subjected to temperatures higher than 120°C, the critical CTOD_{
c} corresponding to maximum load
During this stage of the applied load for all temperatures, corresponding CTOD and effective crack length have increased more than maximum load
Crack propagation stage III.
This situation of loading corresponds to the descending portion of
Crack propagation stage IV.
Similar to (
Linear asymptotic superposition assumption [
The nonlinear characteristic of the
An effective crack consists of an equivalentelastic stressfree crack and equivalentelastic fictitious crack extension.
The equivalentelastic crack length for WS specimen is expressed as [
Experimental results of fracture parameters.
Specimen  Temperature 

CMOD_{ini} 









WS1  20°C  6.19  0.068  8.33  0.174  0.065  15.30  0.53  0.505  1.061  234.15 
WS2  6.28  0.047  9.81  0.120  0.039  20.51  0.48  0.523  1.070  483.66  
WS3  7.26  0.063  10.40  0.210  0.079  20.66  0.57  0.610  1.497  438.22  
WS4  7.02  0.086  7.92  0.152  0.060  18.88  0.56  0.357  1.091  219.39  
WS5  5.65  0.060  9.39  0.237  0.096  15.45  0.54  0.503  1.213  321.05  
Average 













WS6  65°C  6.98  0.055  11.31  0.195  0.078  21.73  0.56  0.550  1.594  425.91 
WS7  3.88  0.050  8.23  0.163  0.100  24.79  0.66  0.303  1.664  482.62  
WS8  6.88  0.078  10.41  0.212  0.087  19.43  0.57  0.557  1.518  487.75  
WS9  7.94  0.052  10.71  0.164  0.087  23.25  0.60  0.511  1.685  480.51  
WS10  6.32  0.056  11.67  0.229  0.086  16.60  0.54  0.562  1.507  522.36  
Average 













WS11  120°C  5.03  0.064  8.37  0.191  0.056  10.65  0.47  0.518  0.900  396.52 
WS13  4.69  0.093  8.25  0.224  0.084  11.87  0.53  0.417  1.058  517.82  
WS12  4.71  0.070  7.53  0.357  0.152  9.48  0.60  0.419  1.202  654.73  
WS14  2.79  0.030  7.53  0.198  0.083  15.42  0.58  0.249  1.107  345.46  
WS15  —  —  —  —  —  —  —  —  —  —  
Average 













WS21  300°C  1.89  0.182  3.40  0.653  0.283  2.45  0.61  0.168  0.556  437.92 
WS22  3.48  0.185  5.53  0.667  0.280  3.49  0.59  0.309  0.841  611.47  
WS23  1.82  0.121  3.38  0.672  0.271  1.91  0.57  0.162  0.480  341.77  
WS24  2.61  0.194  4.97  0.577  0.262  1.99  0.52  0.232  0.589  564.12  
WS25  2.03  0.096  4.17  0.651  0.361  4.03  0.68  0.175  0.913  549.99  
Average 













WS36  450°C  1.52  0.126  3.37  1.009  0.544  1.41  0.62  0.135  0.582  611.53 
WS37  —  —  —  —  —  —  —  —  —  —  
WS38  1.52  0.163  3.26  1.419  0.660  1.46  0.62  0.135  0.527  482.45  
WS39  1.12  0.296  3.07  1.348  0.617  1.34  0.64  0.100  0.563  663.10  
WS40  0.99  0.105  2.94  1.394  0.666  1.58  0.68  0.088  0.659  678.79  
Average 













WS46  600°C  0.76  0.443  1.13  1.482  0.684  0.47  0.65  0.067  0.221  228.23 
WS47  0.53  0.139  1.48  2.082  0.684  0.48  0.64  0.063  0.277  395.06  
WS48  0.81  0.324  1.65  1.908  0.813  1.14  0.76  0.072  0.550  539.22  
WS49  0.58  0.436  1.14  1.687  0.973  0.38  0.65  0.052  0.225  331.99  
WS50  0.62  0.279  1.48  2.082  0.727  0.38  0.62  0.068  0.213  273.07  
Average 










The crack opening displacement at position
The parameters like initiation toughness
The SIF for WS test specimens is written as [
To obtain the complete
Geometry of specimens.
Nine heating temperatures, ranging from 65°C to 600°C (
A closedloop servocontrolled hydraulic jack with a maximum capacity of 1000 kN was employed to conduct the wedge splitting test. Two clipon extensometers were suited at the mouth and the tip of the crack to measure the crack mouth opening displacement (CMOD) and crack tip opening displacement (CTOD). To obtain the complete
Load versus CMOD curves of specimens with temperatures.
The recorded maximum load
Figure
From Table
Since the
When temperatures are less than 200°C, the
Figure
The
On the contrary, the stress intensity factor curve (
Herein, the length of the propagating crack is taken as a horizontal axis, and the crack extension resistance
Stability analysis of crack propagation of various temperatures.
Stability analysis of crack propagation at room temperature
Stability analysis of crack propagation at 120°C
Stability analysis of crack propagation at 300°C
Stability analysis of crack propagation at 450°C
From the initial point
A common character of Figures
Furthermore, it can be seen that when the curve of the stress intensity factor is lower than the crack extension resistance curve, the crack propagates steadily which can be observed in the region between point
The residual crack extension resistance
In the calculation of residual crack extension curves (
For the stability analyses of crack propagation, the comparison between
Equivalentelastic crack length
Critical notch depth of the specimen
Effective crack length corresponding to
Effective crack length corresponding to zero stress of new fictitious fracture zone
Crack mouth opening displacement
Crack tip opening displacement
Residual Young’s modulus
Fracture energy:
Height of wedgesplitting specimens
Crack extension resistance
Cohesive toughness
Cohesive stress at the tip of initial notch
Cohesive stress at equivalentelastic crack length
Maximum load
Crack width at stressfree point
Crack opening displacement at the tip of initial notch
Initial notch depth of the specimen
Crack extension length
Fully developed fictitious fracture zone length
Critical crack mouth opening displacement
Critical crack tip opening displacement
Cohesive force distribution
Tensile strength
Thickness of the clip gauge holder
Initial fracture toughness
Stress intensity factor
Cohesive stress at the break point of softening curve
The initial cracking load
Heating temperatures
Crack width at break point of softening curve.
The authors declare that they have no conflict of interests regarding the publication of this paper.
The State Laboratory of Disaster Reduction in Civil Engineering (SLDRCE09D02) and the Young Scientist Project of Natural Science Foundation of China (NSFC: 51008235) have supported this research.