## 1 Introduction  
The introduction of Additive Manufacturing (AM), more commonly referred to as 3D printing, in the late 1980s has made a significant impact on science and technology and revolutionized the way products are designed and manufactured [1; 2]. As growth is expected to exceed 10 billion dollars for AM products and services by 2020, investments in AM related research and development by both industry and government have surged during the last decade [3; 4]. AM comprises a group of manufacturing techniques all based on a similar working principle: fabricating three-dimensional (3D) parts by successive addition of material layers starting from computer-aided-design (CAD) models or 3D scans of existing objects [2; 5]. Melt extrusion technologies, known as Fused Filament Fabrication (FFF) or Fused Deposition Modeling (FDM(tm)), make up one of the largest groups amongst the polymer-based AM processes, which also include Selective Laser Sintering (SLS), stereolithography (SLA), and material jetting [1; 6]. During FFF, feedstock in the form of a thermoplastic filament is fed by a pinch roller mechanism into a print head consisting of a liquefier, heated above the polymer melting temperature, and a nozzle. The solid portion of the filament acts as a piston, exerting pressure to push the molten polymer out of the liquefier through the smaller print nozzle. While extruding molten polymer, the print head moves in the xy-plane following a prescribed pattern. After completing a layer, the heated build plate moves down one layer height, repeating the process to create a three-dimensional object layer-by-layer [5]. FFF has proven itself as a promising manufacturing technology, especially for low production volumes, allowing customization and freedom-of-design. However, its limited material palette, often inadequate mechanical properties and surface finishing remain major drawbacks [1; 2]. Amorphous thermoplastic polymers, such as ABS, are extensively used in FFF. However, besides having good thermal stability, semi-crystalline thermoplastics often possess considerably better mechanical properties, making them tougher and more deformable compared to amorphous glassy polymers [7; 8]. Hence, FFF with semi-crystalline polymers has found its use in, for example, biomedical applications, including PEEK [9] and PA [10] for the production of customized implants, and PLA [11] and PCL [12; 13] for scaffolds. Nonetheless, semi-crystalline polymers exhibit far greater shrinkage upon cooling in comparison with amorphous plastics due to the considerable volume reduction associated with the formation of ordered, more densely packed regions during crystallization [14]. Crystallization of the extruded polymer melt upon deposition from the print nozzle will lead to anisotropic shrinkage and part warpage due to a build-up of internal stresses. This can severely disturb the dimensional stability of the printed part [15; 16; 17]. To provide the final printed part with adequate mechanical strength, polymer chains should diffuse and re-entangle across the interface between successively deposited layers to successfully weld them together [18]. This molecular interdiffusion can be appropriately described by the reptation model, especially for welding of amorphous polymer interfaces [19; 20]. In the case of semi-crystalline interfaces, crystallization is believed to drastically lower molecular mobility, since polymer chains are confined within the formed crystalline structures [21; 22; 23]. Consequently, it is suggested that crystallization should take place after interlayer diffusion to establish sufficiently strong welds [24]. However, co-crystallization across the interlayer interface is considered to be an excellent reinforcement mechanism during welding of semi-crystalline interfaces [24; 25]. Since both molecular diffusion and crystallization are strongly influenced by temperature, knowledge of the temperature history in a deposited layer is of key importance.