Strengthening by needle-shaped ${\beta }^{\prime \prime }$ precipitates is critical in Al–Mg–Si alloys. Here, the strengthening is studied computationally at the peak-aged condition where precipitate shearing and Orowan looping are usually considered to have equal strengths. Pseudo-random precipitate microstructures are constructed based on experimental precipitate dimensions and volume fractions at peak aging. A Discrete Dislocation Dynamics method is then adapted to compute the Critical Resolved Shear Stress (CRSS) for Orowan looping of dislocations moving through the non-shearable precipitate field. The CRSS for Orowan looping is determined by a typical in-situ precipitate spacing that is smaller than the average spacing and by the dislocation core energy within a radius of $\approx$5b, a factor rarely considered. The matrix misfit stresses, volume fraction, and precipitate shape have small effects on the CRSS. With microstructure and property details introduced as faithfully as possible, the CRSS for Orowan looping using atomistically-calibrated core energies at room temperature is nonetheless $\approx$33% higher than experiments. This suggests that precipitate shearing controls strength, and analyses of (i) forces acting on the precipitates, (ii) misfit stresses inside the precipitates, (iii) first-principles results for the relevant precipitate fault energies, and (iv) simulations that mimic precipitate shearing indicate a shearing CRSS closer to experiments. Thus, Orowan looping only sets an upper bound for the CRSS even at peak aging, and further quantitative progress requires detailed modeling of precipitate shearing.

针状加强 ${\beta }^{\prime \prime }$析出物对Al-Mg-Si合金至关重要。在这里，在峰值时效条件下通过计算研究了强化作用，在该条件下，通常认为析出物剪切和Orowan弯折具有相同的强度。基于实验的沉淀物尺寸和峰时效时的体积分数，构建了伪随机沉淀物微观结构。然后，采用离散位错动力学方法来计算穿过不可剪切沉淀场的位错的Orowan循环的临界分辨剪切应力（CRSS）。Orowan循环的CRSS是由典型的原位沉淀物间距（小于平均间距）和位错核心能量在半径范围内确定的。$\approx$5b，很少考虑的因素。基质失配应力，体积分数和沉淀物形状对CRSS的影响很小。尽可能忠实地介绍微观结构和性能细节，但是在室温下使用原子校准的核心能量进行Orowan循环的CRSS仍然很$\approx$比实验高33％。这表明析出物剪切控制了强度，并分析了（i）作用于析出物的力，（ii）析出物内部的失配应力，（iii）有关析出物断层能量的第一性原理结果，以及（iv）模仿的模拟沉淀物剪切表明CRSS的剪切更接近实验。因此，即使在峰老化时，Orowan循环也仅为CRSS设置了上限，并且进一步的定量进展需要对沉淀物剪切进行详细的建模。