An elastic and an elastoplastic methyl methacrylate polymer, both in the glassy state, have been submitted to mode I fracture characterization with two different tests, the single edge notch bending (SENB) and the double cleavage drilled compression (DCDC) tests. The elastic material toughness was simply assessed by the linear elastic fracture mechanics analysis. For the elastoplastic material, the $J$-integral was computed when the strain fields were available. Moreover, numerical analyses were carried out using finite element simulations with a phase-field damage approach, providing comparison when the $J$-integral had been calculated and estimate otherwise, of the critical energy release rate. For each material, as well as for each test, the values of the critical energy release rate that have been estimated here, are in good agreement with the literature. More interestingly, for the same material, both tests provide with very different estimates of this material parameter, leaving engineers uncertain on which test to choose to asses the material toughness in crack opening mode.