Among the numerous risk factors associated to work-related musculoskeletal disorders (WMSD), repetitive and monotonous movements with light-weight tools are one of the most frequently cited. Such tasks may indeed result in the excessive accumulation of local muscle fatigue, causing severe injuries in human joints. Accordingly, this paper proposes a new whole-body fatigue model to evaluate the cumulative effect of the overloading torque induced on the joints over time by light payloads. The proposed model is then integrated into a human-robot collaboration (HRC) framework to set the timing of a body posture optimisation procedure guided by the robot assistance, by the time fatigue overcomes a threshold in any joint. Our overloading fatigue model is based on an estimation method we developed in a previous work, to monitor joint torque variations due to external forces in real-time. To account for individuals' different perception of fatigue, the fatigue ratio parameter in the model is computed experimentally for each subject. The proposed model is first studied on ten subjects by means of an electromyography analysis. Next, its performance is assessed in a painting task and finally evaluated within the HRC framework, which is proved to be able to reduce the risk of injuries caused by excessive fatigue accumulation.