We have performed 2D-Langevin simulations studying the peak effect (PE) of the critical current taking into account the temperature dependence of the competing forces. We observe and report that the occurrence of the PE results from the competition of vortex-vortex interactions and vortex-pin interactions and thermal fluctuations which have different temperature dependencies. The simulations reveal that the PE can only take place for certain pinning strengths, densities of pinning centers and driving forces, which is in good agreement with experiments. No apparent vortex order-disorder transition is observed across the PE regime. Besides, the PE is a dynamical phenomenon and thermal fluctuations can speed up the process for the formation of the PE.PACS numbers: 74.25. Fy, 74.25.Qt One pronounced phenomenon in type-II superconductors is the so called peak effect (PE), which is the appearance of a peak in the critical current density J c before decreasing to 0 with increasing temperature or field [1]. The PE has widely been observed in a variety of low and high temperature superconductors by different experimental techniques [2], such as transport [3][4][5], magnetization [6,7], and ac-susceptibility [8][9][10]. It was proposed long ago that the PE originated from softening of the elastic moduli of vortex lattice [1], which caused by the competitions between elastic energy E el , pinning energy E pin of vortex lattice and the energy of thermal fluctuations E th [11]. Considering the competition between the strength of vortex lattice and the pinning force of isolated pinning center, Labusch showed that J c > 0 only if the pinning force dominates over the strength of vortex lattice, otherwise J c = 0 [12]. According to the Labusch criterion the weak pinning centers in superconductors cannot pin the vortex lattice. Larkin and Ovchinnikov showed that weak pinning centers can act collectively in the correlation volume V c (=L c R 2 c , where L c and R c are the longitudinal and transverse correlation lengths respectively), where the vortices are of long-range order, reducing much the Labusch criterion [13]. In the collective pinning theory the PE was interpreted as resulting from the abrupt decrease of V c due to the reduction in elastic interaction [14]. The PE was recently shown to appear naturally at the crossover from weak collective to strong pinning [15]. Further calculations showed that the "Bragg glass" phases exist to be a quasi-long-range ordered vortex lattice on a length scale r ≫ R c [2]. Furthermore, the occurrence of PE was explained as evidence for a Bragg glass transition or an order-disorder (OD) transition [2,5,9,16]. The OD transition was suggested to be a thermodynamic phase transition induced by thermal fluctuations or pinning centers [2], which has been confirmed experimentally by the direct structural observation of the vortex lattice, such as small angle neutron scattering (SANS) [9], and muon spin relaxation [17]. Also, the investigation of the reversibility of the OD transition provided st...