Fracture mechanics-based method for prediction of cracking
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This document presents a fracture mechanics-based method to predict cracking in circular and elliptical concrete rings under restrained shrinkage. The study highlights the differences in cracking behavior between the two geometries, finding that elliptical rings can crack faster due to higher restraint. The results suggest that a fictitious temperature field is a reliable approach to simulate concrete shrinkage and assess cracking potential in these structures.
![Material properties
It is found that the average 28-day compressive and
splitting tensile strength of the concrete are 27.21 and 2.96
MPa, respectively.
Age-dependent Equations of mechanical properties, in this
case are determined...
1) Elasticity Modulus in GPa
E(t)=0.0002t3 + 0.0134t2 + 0:3693t + 12.715 [t≤28]
2) Splitting tensile strength, ft, in Mpa
fc(t)=1.82t0.13 [t≤28]](https://image.slidesharecdn.com/fractureconcrete-141120123332-conversion-gate01/85/Fracture-mechanics-based-method-for-prediction-of-cracking-7-320.jpg)
![Conclusion
A fictitious temperature field to simulate the shrinkage of
concrete to investigate the cracking behavior of concrete are
appropriate and reliable.
The maximum circumferential tensile stress in an elliptical
ring is about 3.6 times of that in a circular ring.
For a range of value of the critical crack length
[ >or< 24 mm] cracking tendency of circuler and
elliptical ring is different.](https://image.slidesharecdn.com/fractureconcrete-141120123332-conversion-gate01/85/Fracture-mechanics-based-method-for-prediction-of-cracking-28-320.jpg)
Fracture mechanics-based method for prediction of cracking
- 1. A fracture mechanics-based method for prediction of cracking of circular and elliptical concrete rings under restrained Shrinkage by Wei Dong, Xiangming Zhou , Zhimin Wua Tamonash Jana 001411202019
- 2. Introduction Residual stress development during shrinkage of concrete. Occurance and effect of crack formation. Cracking potential test methods(Plate,Bar,Ring) Why Ring test is preferred?
- 3. Circular ring for Ring Test Long period of time is needed before the first cracking occurs in a restrained circular concrete than elliptical ring due to its geometry. Initial cracking may appear anywhere along the circumference of a circular ring specimen. Restraining effect from the central steel ring to the surrounding concrete ring is uniform. Geometry function depends on Ro/Ri only.
- 4. Elliptical ring for Ring Test Higher degree of restraint can be provided by an elliptical geometry than a circular one. Comparetively short period of time is needed before the first cracking than the circuler one. Crack initiates close to the vertices on the major axis of an elliptical concrete ring. Geometry function depends on their inner major and minor radius-to-outer major and minor radius ratio, i.e. R1/(R1 + d) and R2/(R2 + d).
- 5. Specimen Setup The mix proportions for the concrete is1:1.5:1.5:0.5 (cement:sand:coarse aggregate:water) by weight. Following specimen are prepared. 1. 100 mm-diameter and 200 mm-length cylinders(for measuring mechanical properties of concrete) 2. 75 mm in square and 280 mm in length prisms(for free shrinkage test) 3. Notched beams with the dimensions of (100×100×500 mm3 (for fracture test). 4. Series of circular and elliptical ring specimens. Specimens were covered by a layer of plastic sheet and cured in the normal laboratory environment for 24 h.
- 6. Subsequently, all specimens were de-moulded and moved into an environment chamber with 23°C and 50% relative humidity. Mechanical properties of concrete, including elastic modulus E, splitting tensile strength ft and uniaxial compressive strength fc, were measured from the cylindrical specimens at 1, 3, 7, 14and 28 days. Three specimens tested for each mechanical property at each age.
- 7. Material properties It is found that the average 28-day compressive and splitting tensile strength of the concrete are 27.21 and 2.96 MPa, respectively. Age-dependent Equations of mechanical properties, in this case are determined... 1) Elasticity Modulus in GPa E(t)=0.0002t3 + 0.0134t2 + 0:3693t + 12.715 [t≤28] 2) Splitting tensile strength, ft, in Mpa fc(t)=1.82t0.13 [t≤28]
- 8. 3) Critical Stress Intensity Factor in MPa mm1/2 KIC(t) = 3.92 ln(t) + 12:6 4) Critical Crack Tip Opening Displacement in mm CTODC = 0.029t2 + 1.62t + 3.96 t is the age (unit: day) of concrete..
- 9. Free shrinkage tests Free shrinkage of concrete was measured on concrete prisms. Prisms subjected to drying in 23°C and 50% relative humidity. Longitudinal length change was monitored by a dial gauge, which was then converted into shrinkage strain. Four different exposure conditions, i.e. representing four different A/V ratios, were investigated on concrete prisms: (1) all surfaces sealed, (2) all surface exposed, (3) two side surfaces sealed and (4) three side surfaces sealed. Double-layer aluminum tape was used to seal the surfaces.
- 10. Shrinkage strain of concrete obtained from free shrinkage test
- 11. Restrained shrinkage ring tests Thickness, Major and Minor radius of the elliptical ring is taken 37.5, 150 and 75 mm. Inner radius of the circuler one is taken 150. Four strain gauges were attached, each at one equidistant mid-height, on the inner cylindrical surface of the central restraining steel ring. The top and bottom surfaces of the concrete ring specimens were sealed using two layers of aluminum tape. Ring specimens were finally moved into an environmental chamber for continuous drying under the temperature 23°C and RH 50% till the first crack occurred.
- 12. Cracking of concrete is indicated by the sudden drop in the measured strain, recommended by ASTM. Two concrete ring specimens were tested per geometry. Cracking ages of the circular rings are 14 and 15 days, respectively, for elliptical ones are both 10 days.
- 13. Numerical modelling restrained shrinkage Finite element analyses were carried out using ANSYS code to simulate stress development and calculate stress intensity factor. Unlike circuler rings uniform internal pressure theory is not applicable to elliptical ones. A derived fictitious temperature field is applied to concrete to simulate the shrinkage effect. The elastic modulus and Poisson’s ratio of steel both remain constant as 210 GPa and 0.3. Poisson’s ratio of concrete is set constant as 0.2.
- 14. Derived fictitious temperature drop with respect to A/V ratio for a concrete element
- 16. Crack driving energy rate curve (G-curve) Shrinkage effect is simulated through applying the temperature drop on concrete in numerical analysis. Internal stress is developed in concrete, which is uniformly distributed in a circular ring but non-uniformly distributed in an elliptical ring. For circular ring pressure is Distributed uniformly along its inner circumference, and the value is 0.59 MPa
- 17. Pressure on the elliptical one distributes non-uniformly, with the maxim -um and minimum values being 2.14 MPa and 0.28 Mpa. The stress intensity factor (KI) for the circular and elliptical rings are determined based on the classic fracture mechanics theory
- 18. The fictitious temperature drops are applied on the ring in combined thermal and fracture analysis to simulate the mechanical effect of shrinkage of concrete. Stress intensity factor KI in MPa mm1/2 of the circular ring can be formulated from numerical simulation as While that of the elliptical ring is T (in °C)=fictitious temperature drop, αc =linear thermal expansion coefficient of concrete Energy supplied for crack propagation, i.e. G can be derived by
- 19. G-curves of circular and elliptical rings at various ages
- 20. Resistance curve (R-Curve) Based on the work of Ouyang and Shah.. The R-curve is formulated as α = ac /ao ac = critical crack length, ao =initial crack length, α,β=R curve coefficients, ψ= Resistance parameter
- 21. The values of α and β can be determined by and In this study the R-curves for the circular and elliptical rings were approximately taken as that of an infinite large plate with a Side Edge Notch pre-crack.
- 22. Creep The effect of creep on strain in a ring specimen is not taken into account when using the fictitious temperature drop to simulate the shrinkage effect. But actually cracking of a concrete ring specimen is affected by not only shrinkage but also creep. the total strain is the sum of elastic strain and creep strain and can be expressed as σc (t0)=stress in concrete at the time of loading t0 = modulus of elasticity of concrete at loading time, J(t,t0)=creep function, φ(t,t0)=Creep Coefficient
- 23. Effect of creep on nominal stress
- 24. Effect of creep on nominal stress
- 25. Cracking age The restraining effect provided by the steel ring can be regardedas the externally applied load on concrete. The abrupt strain drop indicates that the applied load has reached its peak. Corresponding crack length a is the critical crack length ac. At the critical state corresponding to a = ac, the G and R curves intersect and have the same slope. i.e. mathematically G = R = (KIC)2/E
- 26. Determination of cracking age for concrete rings
- 27. Determination of cracking age for concrete rings
- 28. Conclusion A fictitious temperature field to simulate the shrinkage of concrete to investigate the cracking behavior of concrete are appropriate and reliable. The maximum circumferential tensile stress in an elliptical ring is about 3.6 times of that in a circular ring. For a range of value of the critical crack length [ >or< 24 mm] cracking tendency of circuler and elliptical ring is different.
- 29. 29 Thank You