Rate- and temperature-dependent ductile-to-brittle fracture transition: Experimental investigation and phase-field analysis for toffee

Research output: Contribution to journalResearch articleContributedpeer-review


The mechanical behaviour of many materials, including polymers or natural materials, significantly depends on the rate of deformation. As a consequence, a rate-dependent ductile-to-brittle fracture transition may be observed. For toffee-like caramel, this effect is particularly pronounced. At room temperature, this confectionery may be extensively deformed at low strain rates, while it can behave highly brittle when the rate of deformation is raised. Likewise, the material behaviour does significantly depend on temperature, and even a slight cooling may cause a significant embrittlement. In this work, a thorough experimental investigation of the rate-dependent deformation and fracture behaviour is presented. In addition, the influence of temperature on the material response is studied. The experimental results form the basis for a phase-field modelling of fracture. In order to derive the governing equations of the model, an incremental variational principle is introduced. By means of the validated model, an analysis of the experimentally observed ductile-to-brittle fracture transition is performed. In particular, the coupling between the highly dissipative deformation behaviour of the bulk material and the rate-dependent fracture resistance is discussed.


Original languageEnglish
Article number109878
JournalEngineering fracture mechanics
Publication statusPublished - Feb 2024

External IDs

Scopus 85183328851
ORCID /0000-0003-3358-1545/work/152543531



  • Fracture, Incremental variational principle, Phase-field, Rate-dependent ductile-to-brittle transition, Toffee