 also been shown to have a rate-independent $\gamma_c$ with some spread (See Fig.13 in \cite{olsson2010slow}). However, that \textit{both} $\gamma_c$ and $\sigma_c$ are insensitive to applied rate of deformation certainly merits discussion. To the best of our knowledge, shear-startup studies for system akin to our surfactant gels haven't been systematically carried out. The study of fracture in complex fluids has however been an active field of research \cite{ligoure2013fractures}. One of the models that is routinely employed to model fracture phenomenon in transient networks is the Activated Bond Rupture (ABR) in which the dissociation of bonds in a network is enhanced due to an applied stress. The model was invoked for the case of polymer gels in \cite{skrzeszewska2010fracture} and it predicts the critical strain for fracture $\gamma_c\sim C_1$ln$(C_2\dot\gamma)$ and thus $\sigma_c\sim C_3$ln$(C_4\dot\gamma)$ ($C_{1-4}$ are material dependent constants) i.e - the rupture strain and stress have a logarithmic dependence on applied rate of deformation. As mentioned before however, no such dependence is found in our experiments. A shear-rate independent rupture strain was found in a lecithin-cyclohexane system that forms a wormlike micellar network \cite{olsson2010slow}, but the shear-stress at rupture strongly depends on $\dot{\gamma}$ in the fracture regime. The authors proposed that the fracture in this system is characterized by a \textit{uniformly} accelerating fracture driven by breakage of micellar strands. Their post-fracture state consists of a nematic phase populated by disentangled and highly aligned micelles. 

\begin{figure}[!h]
	\begin{center}
	
	
		\includegraphics*[width=85mm]{Picture18}
	\end{center}
	\vspace*{-5mm}
	\caption{Shear start-up results post-fracture plotted as $\sigma$ vs shear- strain, $\gamma$\% for 8\% VES solution at different values of $\dot{\gamma}$: Red - 0.03$s^{-1}$, Green - 0.05$s^{-1}$, Blue - 0.1$s^{-1}$, Black - 0.3$s^{-1}$. Inset : Same as main figure but for 4.5\% VES. }
	\label{ss4}
\end{figure} 
This fracture mechanism doesn't apply to our system for two reasons - (1): it is unlikely that micellar breakage plays a role in the fracture as it was argued that for order unity deformations, micellar chains between entanglements store an elastic energy $\sim O(k_bT/l_e)$ \cite{cates1990nonlinear} which for $l_e \sim 50 nm$ is much smaller than the scission energies (even if the effective scission energy is reduced by an applied force). In any case the achieved $\sigma$ in our rheology experiments seem to be much smaller than micellar breaking stresses reported in previous studies \cite{rothstein2003transient,mandal2018stretch} (2): Our results clearly show that after the stress rapidly drops, the sheared material has a distinct \textit{elastic} growth of stress followed by a weak overshoot en-route to the final stress (See Fig.~\ref{ss4}). This points towards an absence of a nematic state as a low viscosity nematic state cannot store an elastic stress \cite{olsson2010slow} and suggests that the post-fracture state is marked by structures that can contribute an elastic stress. In the absence of velocimetry data, we can only conjecture the mechanism of fracture in micellar gels. For $\dot{\gamma}$ in the range of the fracture regime, the micellar network is deformed quickly enough that there isn't enough time for re-arrangements (and re-entanglements) and its original elastic structure is forced to change. Since disentanglement has to occur before the formation of a nematic state, it is likely that the micellar disentanglement drives the eventual fracture of the network. We propose that the network fails by strain localization \cite{cheng2012shear,erk2012extreme}. The sudden drop after attaining a stress peak (Fig.\ref{ss3}) along with the absence of a nematic state of shear-aligned micelles suggests that this is not an homogeneous event as suggested in \cite{olsson2010slow} but a \textit{localized} crack or fracture \cite{berret2001evidence}. If we assume that this localized crack, presumably a region that is entanglement depleted, can then rupture and release stress according to the Griffith's criterion \cite{griffith1921vi}, it completes the picture of the shear-induced fracture dynamics discussed so far. This picture explains a couple of features of our data - (1): The critical rupture stress predicted by the Griffith's criterion, $\sigma_{rup}$ is independent of $\dot\gamma$ and this can explain the insensitivity to $\dot{\gamma}$ seen in our results, (2): $\sigma_{rup}\propto a$, where $a$ is an estimate of the size of the initial micro-crack that eventually leads to fracture. Since we don't have control over $a$ in our experiments and it could likely depend on a number of factors like thermal fluctuations or material history/preparation, this can explain why we see a spread in $\gamma_c,\sigma_c$ in our data. Clearly, there is much to uncover about the failure scenario in this regime. Preliminary experiments suggest that the presence of a fracture can be altered by the nature of rest before imposing a shear-rate. Indeed, such fracture dynamics have been shown to depend on boundary conditions and material history \cite{fielding2021yielding,benzi2021continuum}. Disentangling the role of these in the phenomenon displayed by our micellar gels is out of scope of the present paper. In order to better understand this interesting fracture regime and rule out other possible mechanisms like wall-slip, further detailed studies are required, starting with characterizing the dynamics of these wormlike micellar gels under an imposed shear stress. Such a study is currently underway \cite{gupta2020rheology}. We end this section on shear-rheology with a discussion on `flow-curves' exhibited by VES solutions. 
 
 For flow-curves, we sweep downwards from $\dot{\gamma} = 10^2s^{-1}-10^{-3}s^{-1}$ by adjusting the waiting time at each $\dot{\gamma}$. We report results upto $\dot\gamma = 10^{-3}s^{-1}$ because at lower rates, $\sigma$ takes very long time to reach steady-state. For $\dot\gamma>1s^{-1}$, VES show a marked shear-thinning behaviour, $\eta\sim\dot{\gamma}^{-\alpha}$ or $\sigma\sim\dot{\gamma}^{1-\alpha}$. The average value of the exponent extracted from the data in Fig.~\ref{flowcurve} is $\alpha \simeq 0.72$. To obtain a proper estimate of $\alpha$ would require conducting multiple flow-curve experiments and averaging over independent runs at each $c$, so our estimate of $\alpha$ should at best be looked as a rough estimate. But, we note that this scaling lies somewhere in between $\alpha = 0.77$ and 0.66, which are predictions made for flexible micelles and more rigid micelles respectively \cite{zhang2013mesoscale}. A typical step-down in shear experiment ($\dot{\gamma} = 10^2 -10 s^{-1}$) offers some insight into the state of VES when deformed by a $\dot\gamma$ in the shear-thinning regime. As seen in the bottom inset of Fig.~\ref{flowcurve}, when $\dot{\gamma}$ is stepped down, there is a rapid drop in stress, followed by a build-up to the steady-state stress at $\dot{\gamma} = 10s^{-1}$. This rapid drop indicates that for $\dot{\gamma}$ in this regime, the shear-thinning behaviour arises due to aligned micelles that form a viscous nematic phase which allows stress to relax almost instantaneously when $\dot{\gamma}$ is dropped. The stress build-up post drop-off indicates re-building of stress-bearing microstructure. Taken together, this behaviour is suggestive of a thixotropic response in this regime \cite{mewis2009thixotropy,larson2015constitutive,larson2019review}. We also note that for $\dot\gamma$ between $0.05-1s^{-1}$, the value of $\alpha$ is markedly smaller than that in the shear-thinning regime. This range of $\dot\gamma$ coincides with the range in which we have characterised a fracture behaviour earlier and the transition in the value of $\alpha$ can indicate a structural change in the micelles, the physical mechanism for which remains elusive at this point. 
 
 \begin{figure}[!h]
	\begin{center}
	
	
		\includegraphics*[width=85mm]{Picture19}
	\end{center}
	\vspace*{-5mm}
	\caption{Flow curves for different VES concentration, $c$ - Red - 10\%, Blue - 8\%, Green - 6\%, Black - 4.5\%. In