1. Purdue University School of Civil Engineering West West Lafayette, Indiana Autogenous Shrinkage, Residual Stress, and Cracking In Cementitious Composites: Influence of Internal and External Restraint Jae-Heum Moon, Farshad Rajabipour, Brad Pease, and Jason Weiss 4 th International Seminar on Self-Desiccation and Its Importance in Concrete Technology

2. Introduction We Typically use ‘Effective Properties’

3. Equivalent Strain (  Composite ) ( = 1.405, C 1 = 0.25) Equivalent Strain as determined using Pickett’s Approach from 1956 Pickett’s equation has an awkward computation for n Here results of simulations (hex cell)

4. Equivalent Elastic Modulus (E Composite ) T.C. Hansen developed an approach to estimate the elastic modulus using a similar approach to those described by Pickett (an aggregate sphere in a paste cell). Here we see hexagonal unit cell simulations which compare well

5. Equivalent Residual Stress (  Composite )  Composite  = E Composite  Composite E Paste = 20 GPa, E Agg = 40 ~ 200 GPa  SH-Paste -100  If we neglect creep, we could simulate the effect of restraint (using Picketts and Hansens estimates) as we increase the volume of the aggregate Here we can see that as the volume of aggregate increases the stresses decrease This would imply that the residual stress would decrease

6. Scope of this Research and Objectives Does the presence of aggregate would result in local internal stresses that are different than the stresses obtained from the ‘equivalent property approach’? To evaluate the role of aggregate on the residual stress development as it is influenced by both internal and external restraint To investigate how external restraint changes the shape of the stress field around the aggregate To begin to try to incorporate microcracking and cracking in the composite systems

7. Introduction to the Idea of Residual Stress in a Homogenous System Residual stress development: (For now we will assume no creep effects to keep the problem somewhat straightforward) Externally Unrestrained Homogenous Paste No stress (  paste ) Externally Restrained L Paste L’  L’ Stress (  paste =E paste  paste ) L Paste

8. Residual Stress in a Heterogenous System Residual stress development: (For now we will assume no creep effects to keep the problem somewhat straightforward) Internal Stress  Internal ? L L”  L’’ Stress (  ?) Under External + Internal Restraint L ? Agg.  d Externally Unrestrained Externally Restrained Heterogeneous

9. A Model to Investigate the Residual Stress Fields ANSYS – FEA Model Quadratic rectangular eight-node elements plane-stress Autogenous shrinkage applied using a temperature substitution analogy Paste - assumed to have a modulus of 20 GPa and a Poissons ratio of 0.20 Perfect-bond between aggregate and cement paste is assumed Length (5) to Width (1) E Paste =20 GPa, Paste =0.2, E Agg =200 GPa, Agg =0.3  SH-Paste =-100 

10. Single Aggregate Prism Model - Externally Unrestrained Sample - Internal Stress    : MPa ) Externally unrestrained sample is nearly axi- symmetric

11. Single Aggregate Prism Model - Externally Unrestrained Sample - Internal Stress    : MPa ) Externally unrestrained sample has stress fields which are nearly axi-symmetric

12. Single Aggregate Prism Model - Externally Restrained Sample -    : MPa ) Externally restrained sample exhibits different behavior

13. Single Aggregate Prism Model - Externally Restrained Sample -    : MPa ) Externally restrained sample exhibits different behavior

14. Comparing Single Aggregate Prism Models We can see the stresses perpendicular to the B-Axis in the unrestrained specimen are higher than the other direction

15. Single Aggregate Prism Model (Bond Condition) Agg. Externally Restrained Perfectly Bonded Perfectly Unbonded Externally Unrestrained Perfectly Bonded/Unbonded (Vertical Direction) Stress Localization H B Void No Stress Void Externally Restrained

16. Consider Models with More than One Aggregate Up to now we discussed about the residual stress development in single aggregate systems We have also been studying hexagonal unit cell models to get a better idea of what is happening in the overall system These hexagonal cell models were shown to be similar to the case of restrained ‘ring’ elements in some earlier studies

17. Unit Cell Composite Models (Finite Element Analysis) Unit Cell Composite Model   : MPa ) Externally Unrestrained Externally Restrained

18. Unit Cell Composite Model - Externally Unrestrained - Results indicate that residual stress increases with an increase in –Aggregate Volume –Elastic Modulus of the Aggregate Residual stresses can be high even though the specimen is externally unrestrained This is consistent with the measurement of acoustic activity which may correspond to microcracking

19. Unit Cell Composite Model - Externally Restrained - Results indicate that residual stress is similar with –Agg. Volume –Elastic Modulus of the Aggregate This may suggest that while the stiffness and volume of the aggregate are important for free shrinkage they may be less critical for cases of restrained shrinkage

20. Comparing the Heterogenous Stress and the Homogenous Stress The maximum homogenous stress significantly varies with aggregate volume and stiffness The maximum heterogenous stress does not vary significantly with elastic modulus or aggregate volume This suggests that external restraint in a heterogenous system requires further study

21. The Need to Include Stable Crack Development at the Aggregate Up to now we discussed about the residual stress development It has become clear from both experimental and numerical simulations that microcracking and cracking behavior in a heterogenous composite system are important and would substantially impact modeling We will discuss preliminary model results though substantially more experimental and numerical studies are underway

22. Preliminary Observation BOND CONDITION – MICROCRACKING (Key issue) MicrocrackingCracking (Example: Restrained Boundary Condition)

23. NIST - OOF Simulation Procedure Polished Surface phenolphthalein Define phases Image Analysis Surface Treatment Mesh Material Properties Meshed image Concrete Concrete Specimen Saw Cut Polishing

24. NIST - OOF Simulation (2-Phase: Agg. & Paste) Apply boundary condition, shrinkage strain onto cement paste phase Before cracking After cracking Stress Analysis  1 0 MPa 25 MPa 12 MPa Strain Analysis  1 - 435  467  0  Cracked image After Cracking (Example: Externally restrained B.C.)

25. NIST - OOF Simulation (3-Phase: Agg., Paste, Interface) Interface  Bond Condition 3-Phase Strain Analysis  1 1000  - 435  2-Phase Analysis 0  3-Phase Analysis Paste Aggregate Interface

26. Conclusions The Existence of Aggregate Provides Internal Restraint  Higher Internal Stress Development (  Max-Internal >  Composite ) The Bond Condition Between Aggregate and Cement Paste - Externally Unrestrained  Little role - Externally Restrained  Critical Role of Aggregate on the Internal Stress Development - Externally Unrestrained: Higher V Agg, E Agg  Higher  Max.-Internal - Externally Restrained: Not Clear (But, small changes when E Agg /E paste > 2)

27. Conclusions Equivalent Stress vs. Maximum Internal Stress 1)  Max-Internal >  Composite 2) The increase of V Agg :  Composite Decreases  Max-Internal Does not vary significantly  It is possible to underestimate the microcracking and cracking potential of concrete if estimation is performed only using equivalent parameters Further Information http://bridge.ecn.purdue.edu/~wjweiss