# Pullout Response of Ultra-High-Performance Concrete with Twisted Steel Fibers
## 3 Experimental and Verification
### Experimental Results
#### 3.3.2 Untwisting Mechanism  
The above untwisting phenomenon is found to be related to the pullout force response and is discussed in this section. The eighteen pullout force versus fiber displacement \(P_{f}\)-s curves of specimens with three different embedment lengths were obtained. The results show that these curve patterns are similar and thus the average data lines for each embedment length are shown in Figure 8. The patterns of the pullout curves are generally consistent with those in Figure 1, while the maximum pullout force is around 200-250N that is more than one order of magnitude compared to the typical pullout force values collected from [PERSON] and his coworkers [1]. The compressive strength of UHPRC is 155 MPa, more than approximately 55% higher the value of high-performance concrete tested by [PERSON] and his coworkers. Thus, the ultra-high mechanical property of UHPRC could increase the high pullout force as shown in Figure 7. In addition, the matrix-fiber interface in UHPRC has a high bond strength, which could also contribute the high pullout force.  
Although there are variations of pullout force for the six replicate samples, the general pattern of pullout force-fiber displacement curve shows there are three distinguishable stages that can be identified. Both our pullout experimental data and the testing data from [PERSON] and his coworkers show a similar tri-linear-stage pattern, as shown in Figure 1. The model assumption of our study (Section Modal assumption) is thus reasonable.  
To understand the untwisting mechanism and the pullout mechanism, the three trilinear stages of pullout force versus fiber displacement curves are presented in Figure 7 and analyzed as:  
Figure 6: Comparison of twisted steel fiber shapes before and after pullout.  
Figure 7: Averaged experimental pullout curves.  
* Linear debonding stage: The pullout force increased linearly with the fiber end displacement, similar to the elastic stage for the normal concrete [25]. This process takes around 1-3 min. There is no relative displacement between matrix and TSF, indicating the matrix-fiber interface remains intact with no debonding occurs. Thus, the strong bonding between fiber and its surrounding matrix produces a united resistance to the external pulling force from both TSF and matrix. By the end of this linear process, debonding initiates at the matrix-fiber interface where the pullout force-loading displacement relationship becomes weakly nonlinear.
* Plastic untwisting stage: After the debonding occurs, debonding slip rotation of TSF is believed to start. This movement is a kind of screw-like movements at the embedded fiber part after debonding. As there is no relative rotation at the sample ends due to the constraint from the fixture, a torque is generated. This torque leads to the plastic 'untwisting' deformation in the fiber part near the outlet and thus the stable untwisting pull-out force. This pull-out force hardening stage was also reported by [PERSON] et al. [17]. As shown in Figure 7, there are slight fluctuations in the untwisting pullout force. The fluctuations may result from the inhomogeneity of the matrix-fiber interface and the stress concentration on the rectangular corner of TSF. This stress concentration may be difficult to penetration by the matrix [1]. The super-high strength of matrix prevents the TSF from damaging the matrix due to the undesirable sites of stress concentration.
* Dropping stage: When the remaining embedment length of the fiber is less than the effective untwisting length \(\Delta l\), the pull-out force rapidly decreases to zero when the torque is released.