Concrete cracks pose significant challenges to infrastructure maintenance and safety. Traditional methods for detecting cracks suffer from inefficiency and subjectivity. Deep learning has shown promise recently, yet it often requires extensive labeled data. A semi-supervised concrete crack detection network (SS-CCDN) is proposed to handle the aforementioned challenge. To be specific, a multi-task model that takes edge feature detection of cracks as an auxiliary task is established. This model is then applied to both student and teacher networks to realize semi-supervised detection. Furthermore, the feature fusion networks incorporate the innovative multi-head cosine non-local attention module to achieve comprehensive acquisition and implementation of feature information at different scales. Lastly, the memory module is integrated into the network to compare the commonalities and distinctions between input sample information and memory sample data, successfully and effectively detecting concrete crack areas. SS-CCDN outperforms other baselines in detection, according to experimental results on two benchmark datasets.