Upscaling of Strain-Hardening Cementitious Composites

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“[Strain-hardening cementitious composites (SHCC)] are a new class of [fiber reinforced cementitious] composites characterized by a strain-hardening behavior in tension after first cracking accompanied by multiple cracking up to relatively high strain levels.” In order to contribute to the transition of common relatively thin SHCC elements for lab experiments into applications of large SHCC elements in practice, knowledge and understanding of the mechanical performance of SHCC when upscaling the element size is needed. When varying the element size for materials a differentiation in the nominal strength may be observed. This phenomena is called the size-effect. For concrete many sources of size-effect have been identified and investigated. These include the Wall effect, diffusion processes, hydration heat, statistical inhomogeneities, linear elastic fracture mechanics, and fractal nature of the crack surface. Even though SHCC shares many similarities with ordinary concrete it also has key differences which could lead to other behavior during upscaling of the element size. No inclusion of coarse aggregates, possible dependency on fiber properties, dispersion and orientation, and a ductile nature of failure. In this thesis first it was investigated whether there is a general size-effect for SHCC. The adjective ‘general’ is used because it includes multiple sources of size-effect. Aside of size-effect the strain capacity was also considered, since this is one of the main advantages of using SHCC. To do this a specimen of 120*30*10 mm3 was compared with a specimen of 360*90*30 mm3 in a 4-point bending test (4-PBT). The nominal strength and fictitious strain capacity dropped from respectively 13.3±1.5 MPa to 8.4±0.4 MPa and 8.9±1.6 ‰, to 4.9±2.1 ‰ due to the upscaling. The fictitious strain is a strain calculated based on the deflection of the specimen and linear elasticity. There are many sources of size-effect and it has been decided to investigate the effect of fiber effectivity and fracture mechanics based size-effect. Since fibers play an important role of the behavior of SHCC and fracture based size-effect is a main contributor of size-effect in ordinary concrete. Aside from the findings above there are strong suggestions that increase of the loading (displacement) rate will decrease the nominal strength and strain capacity significantly. Comparison of these two parameters found in literature with different loading rates is not advised. Furthermore a protocol has been developed to characterize the crack width distribution of the cracked SHCC specimen in future research. Fiber effectivity introduced size-effect concerns the dispersion and orientation of the fibers which play a pivotal role in the behavior of SHCC. It is suspected that the commonly used relatively thin SHCC elements for lab experiments might alter the fiber orientation favorably and overestimates the nominal strength and strain capacity compared to thicker elements. To investigate this a SHCC cube of 150*150*150 mm3 was produced where after three differently orientated specimens of 120*30*10 mm3 were sawn out. The nominal strength and strain capacity of these specimen were obtained with a 4-PBT and compared to the values of thin casted specimen of 120*30*10 mm3. To verify whether there is a alterations in fiber orientation by the specimen preparation and to investigate fiber effectivity sections with a thickness of approximately 40 microns were analyzed. It has been verified that fiber orientation has been altered for the specimen sawn from the cube, and that the nominal strength and strain capacity decreased compared with the thin casted elements. Within the three differently orientated specimen one type showed brittle failure opposed to strain-hardening. This type of specimen was vertically orientated in the cube, and surprisingly had comparable fiber effectivity with the other two types of orientated specimen. It was concluded that margin of error in the parameters that describe fiber effectivity is the most important. When a high margin of error is found a higher probability of weak planes in the specimen is present. If a crack initiates at such a plane then brittle failure will occur since the specimens were primarily reinforced with fibers. It is recommended to use steel bars as primarily reinforcement for safety and the fibers for the multiple fine cracks, and to develop a placement method that reduces the margin of error of the fiber effectivity parameters. Fracture mechanics based size-effect is explained by the science of fracture mechanics. For quasi-brittle materials like concrete, increasing the specimen size will shift the material in the linear elastic fracture mechanics zone in the generalized size-effect law, where the nominal strength drops significantly. One study revealed that there is no size-effect in SHCC if there is adequate strain-hardening. However size-effect concerns only the nominal strength, but in SHCC the strain capacity is an more important parameter. Therefor in this thesis, aside from the size-effect, also the effect of upscaling the element size on strain capacity was investigated. This was done by investigating differently sized specimen with , fixed thickness and a fixed specimen height and span ratio. Specimen with spans of 175, 350, 700, and 2100 mm were investigated. It has been found that only the specimen with a span of 2100 mm had a significant drop in nominal strength. This could be explained by an inadequate strain-hardening ability of the used mix design. Furthermore the strain capacity did gradually decrease for each size. This raises major concern since strain capacity is a main advantage of SHCC. A theoretical model has been developed to explain these findings. This model is based on the strength of the material along the crack. Where the strength in the crack tip decreases when it approaches the crack opening where the strain is higher. It was assumed that the crack width increases with element size. With digital image correlation (DIC) technique the crack width has been determined along the height of the localized macro cracks for limited one specimen per span length. The results were corresponding to the assumption with the exception of the specimen with span 700 mm. This might be due to the acquisition of the data, where the cracked side surface was investigated. There is indication that at this specimen of 700 mm a relatively stronger variance in the distribution of the crack width along the specimen thickness was present.